Iaoe?iiaeueia Aeaaeai?y iaoe Oe?a?ie

?inoeooo oai?aoe/ii? o?ceee ?i. I.I.Aiaiethaiaa

OAeE 539.121.23:519.46

?i?aia Ieeiea C?iia?eiae/

I?AAeNOAAEAIIss EAAIOIAEO AEAAA?

O?CE*IEO NEIAO??E OA ?O

CANOINOAAIIss AeI IIENO IAN AAe?II?A

Niaoeiaeueiinoue 01.04.02 – oai?aoe/ia o?ceea

Aaoi?aoa?ao

aeena?oaoei? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oiceei-iaoaiaoe/ieo iaoe

Ee?a — 1999

Aeena?oaoei?th ? ?oeiien.

?iaioa aeeiiaia a ?inoeooo? oai?aoe/ii? o?ceee ?i. I.I.Aiaiethaiaa IAI
Oe?a?ie.

Iaoeiaee ea?iaiee:eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, noa?oee iaoeiaee
ni?a?ia?oiee Aaa?eeee Ieaenaiae? Ieoaeeiae/,

?inoeooo oai?aoe/ii? o?ceee ?i. I.I. Aiaiethaiaa IAI Oe?a?ie, a?aeae?e
iaoaiaoe/ieo iaoiae?a a oai?aoe/i?e o?ceoe?.

Ioioeieii iiiiaioe:aeieoi? o?ceei-iaoaiaoe/ieo iaoe I?E?O?I Aiaoie?e
Ae?aiae/, ?inoeooo iaoaiaoeee IAI Oe?a?ie,

caa. A?aeae?eii i?eeeaaeieo aeine?aeaeaiue,

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe EA*O?EE ?aai ?aaiiae/, Oaoiieia?/iee
oi?aa?neoao Iiae?eey, i. Oiaeueieoeueeee, aeioeaio eaoaae?e oai?aoe/ii?
iaoai?ee.

I?iaiaeia onoaiiaa:Ee?anueeee oiiaa?neoao iiai? Oa?ana Oaa/aiea,
o?ce/iee oaeoeueoao, eaoaae?a eaaioiai? oai?i? iiey

Caoeno aiaeaoaeaoueny «_28_»__aeiaoiy_ 1999 ?ieo ia _11_ aiaeeii ia
caniaeaiii niaoeiaeiciaaii? a/aii? ?aaee Ae 26.191.01 a ?inoeooo?
oai?aoe/ii? o?ceee ?i. I.I. Aiaiethaiaa IAI Oe?a?ie ca aae?anith:
252143, i.Ee?a, aoe.Iao?ieia?/ia, 14a.

C aeena?oaoei?th iiaeia iciaeiieoenue o aiaeiioaoei ?inoeoooo
oai?aoe/ii? o?ceee ?i. I.I. Aiaiethaiaa IAI Oe?a?ie.

Aaoi?aoa?ao ?icineaiee «_9 »__aa?aniy__ 1999 ?ieo.

A/aiee nae?aoa?

niaoeiaeiciaaii? a/aii? ?aaee

aeieoi? o?c.-iao. iaoe

A.?. EOCUeIE*AA

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

A aeena?oaoe?ei?e ?iaio? aea/athoueny i?aaenoaaeaiiy q-aeaoi?iaoe?e
aeaaa? E? a?oi iaa?oaiue, aaee?aeiaeo oa oi?oa?ieo a?oi, ui
a?aeiia?aeathoue ia?aoai?aiiyi n-aei??iiai i?inoi?o. Eaaioia? aeaaa?e,
ye? a?aeiia?aeathoue oi?oa?iei a?oiai E?, canoiniaai? aei ciaoiaeaeaiiy
iiaeo (a?eueo oi/ieo) ianiaeo ni?aa?aeiioaiue aeey ieoaoieo aa??ii?a
JP=1/2+.

Aeooaeuei?noue oaie.

Aeia?a a?aeiii, ui i?eioeei neiao??? a?ae?a?a? aaaeeeao ?ieue o o?ceoe?.
Iniiai? o?ce/i? caeiie, ??aiyiiy ?ooo oa ?o ?ica’ycee, ??ciiiai?oi?
iaoaiaoe/i? iiaeae? o?ce/ieo yaeu iathoue aeayeo neiao??th. Oai??y a?oi,
ye iaoaiaoe/iee aia?ao oai??? neiao??e, oe?iei canoiniao?oueny a
o?ceoe?. I?e oeueiio, e??i aeene?aoieo a?oi, ?icaeyaeathoue
ne?i/aiiiaei??i? oa iane?i/aiiiaei??i? iaia?a?ai? a?oie — a?oie E?,
noia?a?oie ? o.ae.

Cian?i iaaeaaii a?naiae oai??? neiao??? iiiiaieany iiaeie ia’?eoaie:
eaaioiaeie aeaaa?aie oa eaaioiaeie a?oiaie. Oe? iia? ia’?eoe i?eaa?ioee
aei naaa oaaao ye iaoaiaoee?a, oae ? o?cee?a—oai?aoee?a caaaeyee ?o
canoiniaiino? o ??ciiiai?oieo ?icae?eao iaoaiaoeee (oai??y aacenieo
a?ia?aaiiao?e/ieo ooieoe?e, oai??y aoce?a oa ca/aieaiue, iaeiiooaoeaia
aaiiao??y oa ?i.) oa oai?aoe/ii? o?ceee (oai??y ?ioaa?iaieo nenoai,
eiioi?iia ? oiiieia?/ia oai??? iiey, oi/ii ?ica’yci? iiaeae?
noaoenoe/ii? o?ceee, iien ianoaiaea?oieo noaoenoee, oaiiiaiieia?y
?ioaoe?eiiai niaeo?o aeaioaoiiieo iieaeoe oa aeaoi?iiaaieo yaea? oa
?i.).

?icaeoie oe??? aaeoc? a?aeaoaa?oueny a aeaio, iaeiaeiai aaaeeeaeo,
iai?yieao: iaoaiaoe/iiio (aea/aiiy ??cieo aeaoi?iaoe?e aeaaa? neiao??e,
?o i?aaenoaaeaiue oa ?aae?caoe?e) oa o?ce/iiio (iiooe iiaeo canoinoaaiue
eaaioiaeo aeaaa? oa eaaioiaeo a?oi a eiie?aoieo o?ce/ieo caaea/ao). Oea
aecia/a? aeooaeuei?noue oaiaoeee aeena?oaoe?eii? ?iaioe,

ine?eueee inoaiiy oaeoe/ii i?aaenoaaey? iaeaeaa oe? iai?yiee.

A?aeiii, ui eaaioia? a?oie oa eaaioia? aeaaa?e iienothoue neiao???
i?inoi??a c iaeiiooaoeaiith aaiiao???th, a inoaii? iiaeooue
a?aeiia?aeaoe eaaioiaaiiio i?inoi?o—/ano. Oiio, aeey o?ce/iiai
canoinoaaiiy a eaaioia?e a?aa?oaoe?? aaaeeeaeie ? aeaiaioe Eacei??a oa
iaca?aei? i?aaenoaaeaiiy q-aeaoi?iiaaieo aeaaa?, ui a?aeiia?aeathoue
i?oiaiiaeueiei oa aaee?aeiaei a?oiai neiao??? n-aei??iiai i?icoi?o. A
aeena?oaoe?ei?e ?iaio? oea ?iaeoueny aeey q-aeaaa? U’q(son) oa
Uq(ison).

Canoinoaaiiy Aaa?eeeeii, Ea/o?eeii ? Oa?oe/iei eaaioiaeo aeaaa? Uq(sun)
oa Uq(sun,1) (cai?noue sun oa sun,1) a ?ie? aeaaa? aioo??oiuei?
(a?iiaoiai?) oa aeeiai?/ii? neiao??e aeaei iiaeeea?noue, i?e n=4,
iaea?aeaoe aeey aa??ii?a JP=1/2+ i?aaeei noi aeey ?o ian, ui ? ?noioiuei
oi/i?oei aii??e/ii, i?ae a?aeiia i?aaeei noi Aae-Iaia—Ieoai. A
aeena?oaoe?ei?e ?iaio? i?iaaaeaii eeaneo?eaoe?th iaca?aeieo oi?oa?ieo
i?aaenoaaeaiue eaaioiai? aeaaa?e Uq(sun,1). Ia iniia? oe???
eeaneo?eaoe?? io?eiaii ?yae iiaeo ian-ni?aa?aeiioaiue aeey aa??ii?a
JP=1/2+, ui ? q—aiaeiaaie ian-ni?aa?aeiioaiiy Aae—Iaia oa Ieoai.
Na?aae ieo ciaeaeaii ni?aa?aeiioaiiy, yea, i?e ii??aiyii? c aii??e/ieie
ianaie ieoaoieo aa??ii?a, ia? iaeaeuo iiaeeeao oi/i?noue.

Noiniaii o?ce/ii? ?ioa?i?aoaoe?? aeei?enoaiiy q-aeaoi?iaoe?? a
aeena?oaoe?ei?e ?iaio? iieacaii, ia i?eeeaae? aa??ii?a JP=1/2+ oa
JP=3/2+, ui canoinoaaiiy eaaioiaeo aeaaa? a ?ie? aeaaa? a?iiaoiai?
neiao??? aoaeoeaii i?eaiaeeoue aei a?aooaaiiy iae?i?eieo
(iaiie?iii?aeueieo) ii ii?ooaiith oi?oa?ii? SU(3)-neiao??? aeeaae?a a
iane oeeo aa??ii?a.

I?e ia?aoiae? a?ae iienaii? oaiiiaiieia?/ii? iiaeae? aei a?eueo
iine?aeiaii? eaaioiai—iieueiai? iiaeae? iiaea aeyaeoeny ei?eniei
?icaeyae ai?iiieo ?aae?caoe?e eaaioiaeo aeaaa?. Oiio, a aeena?oaoe?ei?e
?iaio?, cai?iiiiiaaii ocaaaeueiaiiy aeey iaai?o n ai?iiieo inoeeeyoi??a
? iiaoaeiaaii eaac?ai?iiio ?aae?caoe?th n-ia?aiao?e/ii? aeaoi?iaoe??
aeaaa?e E? gln.

C i?eeeaaeii? oi/ee ci?o, a aeena?oaoe?? ?icaeyiooi canoinoaaiiy
ai?iiii? ?aae?caoe?? eaaioiaeo aeaaa? aei ciaoiaeaeaiiy ianiaeo
ni?aa?aeiioaiue aeey aaeoi?ieo iacii?a oa aa??ii?a JP=3/2+. Io?eiai?
iania? ni?aa?aeiioaiiy ni?aiaee c oeie, ui ?ai?oa aoee io?eiai? c
aeei?enoaiiyi aaceno Aaeueoaiaea—Oeaoe?ia. Oei naiei aeiaaaeaii
canoiniai?noue ai?iiieo ?aae?caoe?e eaaioiaeo oi?oa?ieo aeaaa? aei
io?eiaiiy ianiaeo ni?aa?aeiioaiue aeey aae?ii?a.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie.

?acoeueoaoe, ui oa?eoee a aeena?oaoe?eio ?iaioo, aoee io?eiai? a ?aieao
ieaiiai? iaoeiai? oaiaoeee a?aeae?eo iaoaiaoe/ieo iaoiae?a a oai?aoe/i?e
o?ceoe? ?inoeoooo oai?aoe/ii? o?ceee IAI Oe?a?ie (oaia «I?aaenoaaeaiiy
eaaioiaeo a?oi ? eae?a?oaaeuei? ?ioaa?iai? aca?iiae??», 1996-2000 ??.).

Iaoa ? caaea/? aeine?aeaeaiiy.

Iaoith aeena?oaoe?eii? ?iaioe ? aiae?c i?aaenoaaeaiue q-aeaoi?iaoe?e
aeaaa? E? oi?oa?ieo, i?oiaiiaeueieo oa aaee?aeiaeo a?oi E?, a oaeiae
canoinoaaiiy q-aeaoi?iiaaieo aeaaa? aei ciaoiaeaeaiiy iiaeo ianiaeo
ni?aa?aeiioaiue aeey aae?ii?a, ye? a iaee a?eueo aenieo oi/i?noue, i?ae
a?aeii? ?ai?oa.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a.

A aeena?oaoe?ei?e ?iaio? aia?oa

1. aeiaaaeaia oai?aia i?i ne?i/aiiiaei??i? i?aaenoaaeaiiy aeaaa?e
U’q(son) (n>5), ui ? ianoaiaea?oiith q-aeaoi?iaoe??th aeaaa?e E? a?oie
iaa?oaiue a n-aei??iiio i?inoi??, oa i?i iane?i/aiiiaei??i?
i?aaenoaaeaiiy aeaaa?e Uq(ison), ui ? ianoaiaea?oiith q-aeaoi?iaoe??th
aeaaa?e E? aaee?aeiai? a?oie a n-aei??iiio i?inoi??;

2. ciaeaeai? aeaiaioe Eacei??a aeey aeaaa? U’q(son) i?e n=4,5,6 oa
aeani? cia/aiiy iia?aoi??a Eacei??a aeaaa?e U’q(so4);

3. aeaii aeaoaeueia aeiaaaeaiiy oiai, ui q-aiaeia iniiaii? iaoi?oa?ii?
na??? caaea? i?aaenoaaeaiiy eaaioiai? aeaaa?e Uq(un,1);

4. io?eiaii an? iiaeeea? iia? ni?aa?aeiioaiiy aeey ian aa??ii?a JP=1/2+
o noai? c q-aeaoi?iiaaieie aeaaa?aie aioo??oiuei? oa aeeiai?/ii?
neiao??e, ye? aeiioneathoue i?ioeaaeo?o aei?noei? o?enaoe?? ia?aiao?a
aeaoi?iaoe??; na?aae ieo ciaeaeaii iioeiaeueia ni?aa?aeiioaiiy (ui ia?
iaeaeuo oi/i?noue);

5. iieacaii, ui aeei?enoaiiy eaaioiaeo aeaaa? o ?ie? aeaaa? a?iiaoiai?
neiao??? aoaeoeaii i?eaiaeeoue aei a?aooaaiiy ?noioiuei iae?i?eieo
(iaiie?iii?aeueieo) iii?aaie ii ii?ooaiith cae/aeii? (iaaeaoi?iiaaii?)
SU(3)-neiao???;

6. cai?iiiiiaaii aaaaoiia?aiao?e/ia ocaaaeueiaiiy aeey iaai?o n ai?iiieo
inoeeeyoi??a ? iiaoaeiaaii eaac?ai?iiio ?aae?caoe?th aaaaoiia?aiao?e/ii?
aeaoi?iaoe?? aeaaa?e Uq;s1,s2,…,s(n-1)(gl(n));

7. i?iaeaiiino?iaaii canoiniai?noue ai?iiii? ?aae?caoe?? q-aeaoi?iiaaieo
oi?oa?ieo aeaaa? aei ciaoiaeaeaiiy ianiaeo ni?aa?aeiioaiue aeey
aaeoi?ieo iacii?a oa aeaeoieaoieo aa??ii?a JP=3/2+.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a.

?acoeueoaoe, io?eiai? a aeena?oaoe??, iathoue oai?aoe/iee oa?aeoa? ?
? aaaeeeaeie, ii-ia?oa, a oai??? i?aaenoaaeaiue q-aeaoi?iiaaieo aeaaa?;
ii-ae?oaa, aeey iiaeaeueiiai aea/aiiy iecueeiaia?aaoe/ieo oa?aeoa?enoee
(oaeeo ye iane) aae?ii?a. Aeei?enoaiiy ai?iiieo ?aae?caoe?e eaaioiaeo
oi?oa?ieo aeaaa? aei io?eiaiiy ianiaeo ni?aa?aeiioaiue aeey aae?ii?a
iiaea aeyaeoeny ei?eniei i?e ia?aoiae? a?ae /enoi oaiiiaiieia?/ii?
iiaeae?, iienaii? a i?ae?icae?e? 2.2, aei a?eueo iine?aeiaii?
eaaioiai—iieueiai? iiaeae?.

Iniaenoee aianie caeiaoaa/a.

O ni?eueieo ioae?eaoe?yo aaoi?ii cai?iiiiiaaii aeiaaaeaiiy oai?aie
i?i ne?i/aiiiaei??i? i?aaenoaaeaiiy aeaaa?e U’q(son) (i?e n>5),
aeiaaaeaiiy oiai, ui q-aiaeia iniiaii? iaoi?oa?ii? na??? caaea?
i?aaenoaaeaiiy eaaioiai? aeaaa?e Uq(un,1); aaoi?ii cae?eniaii
aiae?oe/i? ?ic?aooiee i?e io?eiaii? iiaiiai iaai?o ianiaeo
ni?aa?aeiioaiue aeey aa??ii?a JP=1/2+ oa aiae?oe/i? ?ic?aooiee i?e
aeei?enoaii? ai?iiieo ?aae?caoe?e eaaioiaeo aeaaa? aei ciaoiaeaeaiiy
ianiaeo ni?aa?aeiioaiue aeey aaeoi?ieo iacii?a ? aa??ii?a JP=3/2+. E??i
oiai, aaoi? i?eeiaa o/anoue a iaaiai?aii? anueiai ?ioiai iaoa??aeo
ioae?eaoe?e.

Ai?iaaoe?y ?acoeoao?a aeena?oaoe??.

Iniiai? ?acoeueoaoe aeena?oaoe?eii? ?iaioe aeiiia?aeaeenue ?
iaaiai?thaaeenue ia iaoeiaeo nai?ia?ao ?OO IAI Oe?a?ie (Ee?a,
1995-1998), ia ia?o?e oa ae?oa?e i?aeia?iaeieo eiioa?aioe?yo «Symmetry
in Nonlinear Mathematical Physics» (Ee?a, /a?aaiue 1995; /a?aaiue 1997),
ia i?aeia?iaeiiio neiiic?oi? c iaoaiaoe/ii? oa oai?aoe/ii? o?ceee
«Mathematical Physics — for Today, Priority Technology — for Tomorrow»
(Ee?a, o?aaaiue 1997), ia i?aeia?iaei?e eiioa?aioe?? «Non-Euclidean
Geometry in Modern Physics» (Oaeai?iae, na?iaiue 1997), ia i?aeia?iaei?e
eiioa?aioe?? «Symmetry in Science X» (Aano??y, eeiaiue 1997).

Ioae?eaoe??.

Ca oaiith aeena?oaoe?eii? ?iaioe aeeiiaii 8 ?ia?o, i’youe c yeeo
iioae?eiaai? o aeaeyae? noaoae o iaoeiaeo aeo?iaeao, a o?e aeaeai? ye
iaoa??aee eiioa?aioe?e.

No?oeoo?a oa ianya aeena?oaoe??.

Aeena?oaoe?eia ?iaioa aeeeaaeaia ia 113 noi??ieao; neeaaea?oueny ?c
Anooio, o?ueio ?icae?e?a, Aeniiae?a, Nieneo aeei?enoaieo aeaea?ae c 77
iaeiaioaaiue oa Aeiaeaoea (4 noi?.).

INIIAIEE CI?NO

O Anooi? iaa?oioiaaii aeooaeuei?noue oaie aeena?oaoe?? ? noi?ioeueiaaii
iaoo ?iaioe. Aena?oeaii o?ae ?icaeoeo oai??? i?aaenoaaeaiue eaaioiaeo
aeaaa? o ca’yceo c ?o canoinoaaiiyi o o?ceoe?. Aeaii iaeyae e?oa?aoo?e c
oeeo ieoaiue ? aecia/aii i?noea aeine?aeaeaiue, ye? ?icaeyaeathoueny a
aeena?oaoe??, na?aae ?ioeo ?ia?o. Iiaeaii caaaeueio oa?aeoa?enoeeo
aeena?oaoe??, aeeeaaeaii ei?ioeee ci?no eiaeiiai ?icae?eo,
noi?ioeueiaaii iniiai? iieiaeaiiy, ye? aeiinyoueny ia caoeno.

O ia?oiio ?icae?e? — «q-Aeaoi?iaoe?y U’q(son) aeaaa?e E? so(n) a?oie
iaa?oaiue» — ?icaeyaeathoueny aeaaa?e, ui ? ianoaiaea?oieie
q-aeaoi?iaoe?yie aeaaa? E? a?oie iaa?oaiue SO(n) oa a?oie ?oo?a ISO(n)
n-aei??iiai i?inoi?o, a?aeiia?aeii, oa ?o i?aaenoaaeaiiy.

A i?ae?icae?e? 1.1 ?icaeyiooi anioe?aoeaio aeaaa?o U’q(son), yea ?
ianoaiaea?oiith aeaoi?iaoe??th (a?aei?iiith a?ae aeaoi?iaoe??
Ae??ioaeueaea—Aeae?iai) oi?aa?naeueii? iai?ooth/i? aeaaa?e U(so(n,C))
aeaaa?e E? so(n,C), oa iienai? ?? ne?i/aiiiaei??i? i?aaenoaaeaiiy
eeane/iiai oeio.

Aeaaa?a U’q(son) — oea eiiieaenia anioe?aoeaia aeaaa?a c n-1
ii?iaeaeoth/eieie aeaiaioaie I21, I32, … , In,n-1, ye?
caaeia?eueiythoue aecia/aeueiei ni?aa?aeiioaiiyi

Ij,j-12 Ij-1,j-2 + Ij-1,j-2 Ij,j-12 — [2]q Ij,j-1 Ij-1,j-2 Ij,j-1 =
-Ij-1,j-2, (1)

Ij-1,j-22Ij,j-1 + Ij,j-1Ij-1,j-22 -[2]q Ij-1,j-2 Ij,j-1Ij-1,j-2 =
-Ij,j-1, (2)

[ Ii,i-1 , Ij,j-1] = 0 , yeui | i-j | >1,
(3)

aea /a?ac

[x]q = [x] = ( qx — q-x ) / (q-q-1) , x C
(4)

iicia/aii q-/enei, ui a?aeiia?aea? /eneo x, a q — ia?aiao?
aeaoi?iaoe?? (qC, q0,1). Eiee q1 (‘eeane/ia’ a?aieoey), oi q-/enei [x]q
ia?aoiaeeoue a x.

Aeey oiai, uia iienaoe aacen a U’q(son), ?icaeyiaii ianooii? aeaiaioe a
oe?e aeaaa?? (aaaaea?ii, ui k > l+1, nk,l1)

q1/2Il+1,l Ik,l+1 — q-1/2Ik,l+1 Il+1,l Ik,l
(5)

?acii c ioioiaeiaiiyi Ik+1,k I+k+1,k I+k+1,k. Aaaaeaii eaeneeia?ao?/iee
ii?yaeie aeey oeeo aeaiaio?a o a?aeiia?aeiino? aei ?o ?iaeaen?a. Aoaeaii
iaceaaoe aeayeee aeaiaio c U’q(son) aii?yaeeiaaiei iiiiiii, yeui a?i ?
aeiaooeii ianiaaeath/i? iine?aeiaiino? aeaiaio?a I..+. A
aeena?oaoe?ei?e ?iaio? aeiaiaeeoueny (Oai?aia 1.1), ui iaa?? an?o
aii?yaeeiaaieo iiiii?a ? aacenii Ioaiea?a—A??oaioa—A?ooa a aeaaa??
U’q(son).

Ne?i/aiiiaei??i? i?aaenoaaeaiiy aeaaa? U’q(son), ye? a?aeiia?aeathoue
i?aaenoaaeaiiyi so(n,C), (i?aaenoaaeaiiy eeane/iiai oeio) o q-aiaeic?
oi?iae?cio Aaeueoaiaea-Oeaoe?ia (AOe) caaeathoueny neaiaoo?aie —
iaai?aie mn ?c [n/2] eiiiiiaio m1,n, m2,n,…, m[n/2],n (ooo /a?ac [n/2]
iicia/aii oe?eo /anoeio n/2, ye? caaeia?eueiythoue oiia? aeii?iaioiino?,
a?aeiia?aeii, aeey n=2p+1 oa n=2p. Ca aacen i?inoi?o i?aaenoaaeaiiy ie
a?cueiaii q-aiaeia aacena AOe c aeaiaioaie, iicia/aieie noaiaie AOe

aea eiiiiiaioe mn oa mn-1 caaeia?eueiythoue a?aeiiei oiiaai aaeoaeaiiy.
Aaceniee aeaiaio, iicia/aiee noaiith n, iicia/eii ye |n >.

Iia?aoi? I2p+1,2p i?aaenoaaeaiiy, caaeaiiai iaai?ii m2p+1,
aeaaa?eUq(so2p+1) ae?? ia aaceni? aeaiaioe AOe, iicia/aieo noaiaie (6),
a?aeiia?aeii aei (ooo =2p-1)

? iia?aoi? I2p,2p-1i?aaenoaaeaiiy, caaeaiiai iaai?ii m2p, aeaaa?e
Uq(so2p) ae?? ye (ooo =2p)

A oeeo oi?ioeao mn+j icia/a?, ui eiiiiiaioo mj,n a neaiaoo?? mn
iio??aii cai?ieoe ia mj,n+1; iao?e/i? aeaiaioe Aj2p, Bj2p-1, C2p-1
aeathoueny ae?acaie, ye? caeaaeaoue a?ae q-oaeoi??a, oaeeo ye
[li,2p+1+lj,2p], [li,2p-lj,2p-1], [li,2p+lj,2p-1] oa ?i. Caoaaaeeii, ui
iao?e/i? aeaiaioe Bj2p-1 oa C2p-1 ? ‘i?i?iaeueiith’ aeaoi?iaoe??th
‘eeane/ieo’ (oiaoi i?e q=1) iao?e/ieo aeaiaio?a. Iaeiae, caaaeyee
iayaiino? iao?ea?aeueiiai iiiaeieea d(lj,2p) a Aj2p, yeee ia?aoiaeeoue a
1/2 i?e q->1, oe? iao?e/i? aeaiaioe a?ae??ciythoueny a?ae ‘i?i?iaeueii?’
aeaoi?iaoe??.

A aeena?oaoe?ei?e ?iaio? aeiaiaeeoueny (Oai?aia 1.2), ui iia?aoi?e
Ik,k-1, k=2,…,n, i?aaenoaaeaiiy c neaiaoo?ith mn, ye? caaeai? o
q-aiaeic? aaceno AOe (6) oi?ioeaie ae?? (7)-(8) caaeia?eueiythoue
ni?aa?aeiioaiiyi (1)-(3) aeaaa?e U’q(son) ? aecia/athoue
ne?i/aiiiaei??i? i?aaenoaaeaiiy oe??? aeaaa?e. Eiee q ia ? ei?aiai c
iaeeieoe?, oe? i?aaenoaaeaiiy ? iaca?aeieie.

E??i oiai, yeui q=eh, h R, oe? iia?aoi?e aecia/athoue *-i?aaenoaaeaiiy
ae?enii? ‘eiiiaeoii?’ oi?ie U’q(son).

O i?ae?icae?e? 1.2 ciaeaeaii oi?ioeo aeey eaaae?aoe/ieo aeaiaio?a
Eacei??a aeaaa?e U’q(son), yea ? yaii neiao?e/iith a?aeiinii cai?ie
ia?aiao?a aeaoi?iaoe?? q->q-1. Aeaii yaii aeaiaioe Eacei??a aeueo
ii?yaee?a aeey aeaaa? U’q(son), n=4,5,6. Ia?aoiaaii aeani? cia/aiiy
iia?aoi??a Eacei??a aeey aeaaa? U’q(so(3,C)) oa U’q(so(4,C)) o
i?aaenoaaeaiiyo, iienaieo Oai?aiith 1.2.

Iaaaaeaii, aeey i?eeeaaeo, yai? ae?ace aeey aeueo (i?ae eaaae?aoe/i?)
aeaiaio?a Eacei??a aeaaa? U’q(son), n=4,5. Iaoae (aeea.(5))

X+i,j,k,l =q-1 Iji Ilk — Iki Ilj
+q Ikj Ili

Oiae? aeey aeaaa?e U’q(so(4,C)) ia?ii: C(4)=X1,2,3,4. A aeey aeaaa?e
U’q(so(5,C)) ia?ii:

O i?ae?icae?e? 1.3 iaoiaeii eiio?aeoe?? ?iiith—A?aia?a, canoiniaaiei
aei aeaaa?e U’q(so(n+1,C)), io?eiaii (a a?e?i?eiiio oi?ioethaaii?)
aeaaa?o Uq(ison), yea ? ianoaiaea?oiith q-aeaoi?iaoe??th aeaaa?e E?
iso(n,C) a?oie ?oo?a n-aei??iiai i?inoi?o. Aeaii yaiee ae?ac aeey
eaaae?aoe/ieo aeaiaio?a Eacei??a iaiaeii??aeii? aeaaa?e Uq(ison).
Aeiaaaeaii oai?aio (aiaeia?/io Oai?ai? 1.2) i?i iane?i/aiiiaei??i?
i?aaenoaaeaiiy aeaaa?e Uq(ison), ye? ? q-aeaoi?iaoe??th
iane?i/aiiiaei??ieo i?aaenoaaeaiue aeaaa?e E? iso(n,C). Aeaii oiiae ia
ia?aiao? aeaoi?iaoe??, i?e yeeo oe? i?aaenoaaeaiiy ? *-i?aaenoaaeaiiyie
ae?enii? ‘eiiiaeoii?’ oi?ie Uq(ison) (Oai?aia 1.3).

Ae?oaee ?icae?e aeena?oaoe??, yeee iaceaa?oueny «Eaaioia? aeaaa?e
Uq(un) i Uq(un,1) oa ?o canoinoaaiiy o o?ceoe? aae?ii?a», i?enay/aii
aea/aiith iaca?aeieo oa *-i?aaenoaaeaiue ‘iaeiiiaeoii?’ ae?enii? oi?ie
Uq(un,1) eaaioiai? aeaaa?e Uq(gl(n+1,C)), ?o canoinoaaiith aei
ciaoiaeaeaiiy iiaeo i?aaee noi aeey ian aae?ii?a ia iniia? aeei?enoaiiy
?aea? i?i q-aeaoi?iiaaio a?iiaoiao neiao??th aae?ii?a.

O i?ae?icae?e? 2.1 aeaii aeiaaaeaiiy oiai, ui q-aiaeia iniiaii?
iaoi?oa?ii? na??? ae?enii caaea? i?aaenoaaeaiiy eaaioiai? aeaaa?e
Uq(un,1) (Oai?aia 2.1). Oea aeicaieeei, ca aeiiiiiaith i?ioeaaeo?e
aiaeia?/ii? aei iaaeaoi?iiaaiiai aeiaaeea, eeaneo?eoaaoe iaca?aei?
i?aaenoaaeaiiy c iiiaeeie iaca?aeieo i?aaenoaaeaiue iniiaii? na???
(Oai?aia 2.2) oa iaca?aeieo eiiiiiaio ca?aeieo i?aaenoaaeaiue iniiaii?
na??? (Oai?aia 2.3). Aeae?eaii an? iaca?aei? *-i?aaenoaaeaiiy aeaaa?e
Uq(un,1) (Oai?aia 2.4, Oai?aia 2.5).

I?ae?icae?e 2.2 i?enay/aiee iiaeaeueo?e ?ic?iaoe? i?aeoiaeo, ui
aeei?enoiao? ?aeath i?i q-aeaoi?iiaai?noue a?iiaoiaeo neiao??e aae?ii?a
aeey ciaoiaeaeaiiy iiaeo i?aaee noi aeey ian aa??ii?a JP=1/2+.
I?eeia?oueny, ui aa??iie eeaneo?eothoueny ii i?aaenoaaeaiiyo aeaaa?e
aioo??oiuei? neiao??? Uq(u3), a a ?ie? aeaaa?e aeeiai?/ii? neiao???
aeei?enoaii eaaioia? ‘eiiiaeoi?’ oa ‘iaeiiiaeoi?’ aeaaa?e Uq(u5) oa
Uq(u4,1). Ianiaee iia?aoi?, yeee ii?ooo? aioo??oith neiao??th,
aeae?a?oueny o aeaeyae? aiaeia?/iiio aei ianiaiai iia?aoi?a
iaaeaoi?iiaaiiai aeiaaeea. Ia iniia? eeaneo?eaoe?? oi?oa?ieo
i?aaenoaaeaiue aeaaa?: ‘eiiiaeoii?’ Uq(u5) oa ‘iaeiiiaeoii?’ Uq(u4,1)
(oi?oa?i? i?aaenoaaeaiiy inoaiiuei? iienai? a Oai?ai? 2.4 c i?ae?icae?eo
2.1), ciaeaeaii q-aiaeia a?aeiiiai i?aaeea noi Aae-Iaia—Ieoai aeey ian
aa??ii?a JP=1/2+. Aea?aii niin?a o?enaoe?? ia?aiao?a q ioeyie iaaiiai
iie?iiia; a?i aea? ?yae i?aaee noi aeey ian oeeo aa??ii?a. Iaee?aua c
ieo,

MN+[3]q_7/[2]q_7 M= [3]q_7/[2]q_7 M+M,

aea [2]q_7=2 cos (/7), [3]q_7=[2]q_72-1, ia? oi/i?noue (i?e
i?aenoaiiaoe? aii??e/ieo aeaieo aeey ian aa??ii?a JP=1/2+) i?eaeecii
0.07 %. Aeey ii??aiyiiy, oi/i?noue ianiaiai ni?aa?aeiioaiiy
Aae-Iaia—Ieoai 2 MN+2 M= 3 M + M ? 0.58 %.

O i?ae?icae?e? 2.3, ia i?eeeaae? aa??ii?a JP=1/2+ oa JP=3/2+, iieacaii,
ui aeei?enoaiiy eaaioiaeo aeaaa? a ?ie? aeaaa? a?iiaoiai? neiao???
aoaeoeaii i?eaiaeeoue aei a?aooaaiiy iae?i?eieo (iaiie?iii?aeueieo) ii
ii?ooaiith oi?oa?ii? SU(3)-neiao??? aeeaae?a a iane oeeo aa??ii?a. Aeaii
ii??aiyiiy ?iceeaaeo Ieoai (iiaiiai ?iceeaaeo ii ii?ooaiith SU(3)) c
ia?oei ii?yaeeii ii ii?ooaiith Uq(su3), ?iceeaaeaiiio ca ia?aiao?ii h
(q=eh) a ieie? h=0

(«a ieie?» iaaeaoi?iiaaii? aeaaa?e su3). Iieacaii, ui oe? aeaa ?iceeaaee
ocaiaeaeai?, oi/a ? ia oioiaei?.

I?i?ethno?o?ii oea ia aeaeoieao? aa??ii?a JP=3/2+. O aeeiai?/iiio
i?aaenoaaeaii? c? noa?oith aaaith [p+4,p,p,p,p] aeaaa?e Uq(u5), aeey ian
?ciioeueoeieao?a aa??ii?a ia?ii ae?ace (iaoooth/e aeaeo?iiaai?oiei
?icuaieaiiyi ian a eiaeiiio ?ciioeueoeieao?):

M = M10+ ,

M * = M10 + + [2] ,

M* = M10+ [2] + [3] ,

M = M10+[3] + [4] ,

aea M10 , oa — aeaye? eiinoaioe. Ine?eueee eiaeiee ?ciioeueoeieao c
aeaeoieaoo aa??ii?a iaeiicia/ii o?eno?oueny cia/aiiyi aeeaiino? (aai
a?ia?ca?yaeo – Y ), an? oe? ae?ace iiaeooue aooe caienaieie iaei??th
ianiaith oi?ioeith

MB_i*= M10+ [1-Y] + [2-Y],

aea Bi* i?ia?aa? /ioe?e ??cieo ?ciioeueoeieaoe a 10-ieao?. ?c aecia/aiiy
q-/enae (4) aeieeaa?, ui caeaaei?noue iaio aaee/ei [1-Y], [2-Y] a?ae
a?ia?ca?yaeo Y ?noioiuei iae?i?eia (? noa? e?i?eiith o?eueee a eeane/i?e
a?aieoe? q -> 1), a oea a?aeiia?aea? a?aooaaiith iae?i?eieo ii
ii?ooaiith oi?oa?ii? SU(3)-neiao??? aeeaae?a a iane aa??ii?a JP=3/2+.

O i?ae?icae?e? 2.4 ia iniia? oaoi?ee q-oaici?ieo iia?aoi??a iiaoaeiaaii
ianiaee iia?aoi?, q-eiaa??aioiee a?aeiinii eaaioiai? aeaaa?e Uq(u3) (a?i
a?ae??ciy?oueny a?ae ianiaiai iia?aoi?a, ui aeei?enoiaoaaany a
iiia?aaei?o ?icaeyaeao). A ?acoeueoao? io?eiaii ianiaa ni?aa?aeiioaiiy
[2] (q-1 MN+ q M ) = [3] M + M , yea, ia a?aei?io a?ae iiia?aaei?o
ni?aa?aeiioaiue aeey ian, a?eueo i?inoa ?, e??i oiai, ia caeaaeeoue a?ae
i?aaenoaaeaiiy aeeiai?/ii? aeaaa?e neiao???. Iaeiae, eiai ocaiaeaeaiiy c
aii??e/ieie ianaie aa??ii?a iio?aao? ‘i?aeaiii/ii?’ i?ioeaaeo?e aeey
o?enaoe?? ia?aiao?a aeaoi?iaoe?? q, oiae? ye iiia?aaei? iania?
ni?aa?aeiioaiiy aeiioneaee i?ioeaaeo?o ‘aei?noei?’ o?enaoe?? ia?aiao?a
q ioeyie oe?eeii iaaiiai iie?iiia.

O?ao?e ?icae?e aeena?oaoe?eii? ?iaioe ia? iacao «Ai?iii?
?aae?caoe?? eaaioiaeo aeaaa? oa ?o canoinoaaiiy». A iueiio aeaii
ei?ioeee iaeyae iaiao?aeiiai iaoa??aeo (a?aeiiiai c ?ioeo ?ia?o)
noiniaii ai?ii?a: aecia/aiiy ai?iiieo inoeeeyoi??a ia aeaiaei??i?e
a?aooe? oa ai?iiieo ?aae?caoe?e eaaioiaeo aeaaa? Uq(sun). Aeae? iienaii
iia? ?acoeueoaoe i?i canoinoaaiiy ai?iiieo ?aae?caoe?e eaaioiaeo
oi?oa?ieo aeaaa? aei ciaoiaeaeaiiy ianiaeo ni?aa?aeiioaiue aeey
aaeoi?ieo iacii?a oa aa??ii?a JP=3/2+.

Aeaii aecia/aiiy ai?iiieo iia?aoi??a. ?icaeyiaii aeaiaei??io a?aoeo c
eaaae?aoieie eii??eaie. Eiaeiiio aoceo x oe??? a?aoee iinoaaeii o
a?aeiia?aei?noue iia?aoi?e cieuaiiy oa ia?iaeaeaiiy ci(x), ci+(x),
i=1,…,n, (ye? caaeia?eueiythoue eaiii?/iei aioeeiiooaoe?eiei
ni?aa?aeiioaiiyi) n ??cieo iiae (ni?o?a) oa?i?iiieo
caoaeaeaiue.Iia?aoi? aacii?yaeeo aaiaeeoueny ianooiiei /eiii:

aea x (x, y) — eooiaa ooieoe?y, ? noioaaiiy i?iaiaeeoueny ii an?o
aoceao y a?aoee, oaeeo ui yx, iaceaa?oueny ia?aiao?ii noaoenoeee.
Ai?iii? inoeeeyoi?e ai(x), i=1,…,n, aecia/athoueny ca oi?ioeaie ai(x)
= Ki (x) ci(x) (noioaaiiy ii i a?aenooi?). Ca aeiiiiiaith aaaaeaieo
ai?iiieo iia?aoi??a a ?iaio? O?ao, Ea?aee ? Oooi iiaoaeiaaii
?aae?caoe?th eaaioiai? aeaaa?e Uq(sun). I?e oeueiio ia?aiao? noaoenoeee
ca’yco?oueny c ia?aiao?ii aeaoi?iaoe?? q /a?ac ni?aa?aeiioaiiy q=ei.
Aeaoaeueiee iaeyae oeueiai iaoa??aeo aeaii a i?ae?icae?e? 3.1.

O i?ae?icae?e? 3.2 aeena?oaoe?? ?icaeyiooi i?ea?iaeueio eaac?ai?iiio
(eaac?ai?iie — aeayea niaoe?aeueii neiino?oeiaaia iiaeeo?eaoe?y
ai?ii?a) ?aae?caoe?th aaaaoiia?aiao?e/ii? aeaoi?iaoe??
Uq;s_1,s_2,…,s_n-1(gl(n)) aeaaa?e E? gl(n). Oey aaaaoiia?aiao?e/ia
aeaoi?iaoe?y iiaea aooe io?eiaia ca aeiiiiiaith oa?no?ia—i?ioeaaeo?e ?c
noaiaea?oii? aeaoi?iaoe?? Uq(gln). O /anoeiaiio aeiaaeeo s1=s2=…=sn-1=
s aeaaa?a Uq;s(1),s(2),…,s(n-1)(gl(n)) ia?aoiaeeoue o aeaaa?o
Uq,s(gl(n)), yeo ?ai?oa ?icaeyaeaa Oaeao/? (inoaiiy i?e s=1 ia?aoiaeeoue
a Uq(gl(n)). Eaac?ai?iii? iia?aoi?e ia?iaeaeaiiy oa cieuaiiy, ye?
i?eeiathoue o/anoue o iiaoaeia? ?aae?caoe?? aeaaa?e Uq;s1,s2,…,s(n-1)
(gl(n)), a?ae??ciythoueny a?ae cae/aeieo ai?iiieo iia?aoi??a oei, ui
??ci? ?o iiaee ia ? iacaeaaeieie (ei?aeyoe?y ??cieo iiae
oa?aeoa?eco?oueny ia?aiao?aie s1,s2,…,sn-1, ye? yaii aoiaeyoue a
ia?anoaiiai/i? ni?aa?aeiioaiiy aeey ?o eaac?ai?iiieo iia?aoi??a).

I?e ia?aoiae? a?ae oaiiiaiieia?/ii? iiaeae?, ui aeei?enoiao?oueny a
i?ae?icae?e? 2.2, aei a?eueo iine?aeiaii? eaaioiai—iieueiai? iiaeae?
iiaea aeyaeoeny ei?eniei ?icaeyae ai?iiieo ?aae?caoe?e eaaioiaeo aeaaa?.
A i?ae?icae?e? 3.3 aeena?oaoe?? ?icaeyiooi canoinoaaiiy ai?iiii?
?aae?caoe?? eaaioiaeo aeaaa? aei ciaoiaeaeaiiy ianiaeo ni?aa?aeiioaiue
aeey aaeoi?ieo iacii?a oa aa??ii?a JP=3/2+. Aeey oeueiai nii/aoeo yaii
iiaoaeiaai? aacene o i?inoi?ao iaiao?aeieo i?aaenoaaeaiue eaaioiaeo
aeaaa? ? ciaeaeaii a?aeiia?aei?noue i?ae aae?iiaie oa noaiaie o
oie?anueeiio i?inoi?? ai?iiieo caoaeaeaiue. Iaaaaeaii oaeo
a?aeiia?aei?noue aeey aeayeeo aae?ii?a:

Ia iniia? ianiaiai iia?aoi?a a ai?iii?e ?aae?caoe?? i?iaaaeaii
ia/eneaiiy ae?ac?a aeey ian aae?ii?a. ?acoeueoaoe ni?aiaee c oeie, ui
?ai?oa aoee io?eiai? ia iniia? oi?iae?cio Aaeueoaiaea—Oeaoe?ia. Oei
naiei aeiaaaeaii canoiniai?noue ai?iiieo ?aae?caoe?e eaaioiaeo
oi?oa?ieo aeaaa? aei io?eiaiiy ianiaeo ni?aa?aeiioaiue aeey aae?ii?a.

Ia?aoo?, o Aeniiaeao iaaaaeaii iniiai? ?acoeueoaoe aeena?oaoe?eii?
?iaioe oa ?aeiiaiaeaoe?? uiaei ?o aeei?enoaiiy.

O Aeiaeaoeo, yeee iaceaa?oueny «Aeiaaaeaiiy ni?aa?aeiioaiiy (1.25)»,
aea?oueny aeaoaeueia aeiaaaeaiiy ni?aa?aeiioaiiy (1.25), yea
aeei?enoiao?oueny i?e aeiaaaeaii? Oai?aie 1.2 c ia?oiai ?icae?eo
aeena?oaoe??.

AENIIAEE

1. Aeey aeaaa? U’q(so(n)) oa Uq(iso(n)), ui ? ianoaiaea?oieie
q-aeaoi?iaoe?yieaeaaa? E?, a?aeiia?aeii,a?oie iaa?oaiue SO(n) oa a?oie
?oo?a ISO(n) n-aei??iiai i?inoi?o, aeey n>5 aeaii aeiaaaeaiiy oiai, ui
iia?aoi?e, ye? ? eaac?-i?i?iaeueiith aeaoi?iaoe??th iia?aoi??a eeane/ieo
i?aaenoaaeaiue a aacen? Aaeueoaiaea—Oeaoe?ia, ae?enii caaeathoue
i?aaenoaaeaiiy oeeo q-aeaaa?. Oeae ?acoeueoao ? ua iaeiei
i?aeoaa?aeaeaiiyi canoiniaiino? q-aiaeiaa oi?iae?cio
Aaeueoaiaea—Oeaoe?ia aei iiaoaeiae i?aaenoaaeaiue q-aeaoi?iiaaieo
aeaaa?.

2. Ciaeaeaii o yaiiio aeaeyae? aeaiaioe Eacei??a aeueo ii?yaee?a aeey
aeaaa? U’q(so(n)), n=4,5,6. O aeiaaeeo aeaaa?e U’q(so(4,C)) ia/eneaii
aeani? cia/aiiy iia?aoi??a Eacei??a.

3. Aeaii aeiaaaeaiiy oiai, ui q-aiaeia iniiaii? iaoi?oa?ii? na???
ae?enii caaea? i?aaenoaaeaiiy eaaioiai? aeaaa?e Uq(u(n,1)). Oea
aeicaieeei, ca aeiiiiiaith i?ioeaaeo?e aiaeia?/ii? aei iaaeaoi?iiaaiiai
aeiaaeea, ciaeoe an? iaca?aei? oa *—i?aaenoaaeaiiy eaaioiai? aeaaa?e
Uq(u(n,1)).

4. Ia iniia? eeaneo?eaoe?? iaca?aeieo *—i?aaenoaaeaiue aeaaa?e
Uq(u(4,1)) oa ne?i/aiiiaei??ieo iaca?aeieo i?aaenoaaeaiue aeaaa?e
Uq(u(5)) io?eiaii ?yae iiaeo ianiaeo ni?aa?aeiioaiue aeey aa??ii?a
JP=1/2+, ui ? q—aiaeiaaie ianiaiai ni?aa?aeiioaiiy Aae—Iaia oa Ieoai.
Na?aae ieo, i?e ii??aiyii? c aii??e/ieie cia/aiiyie ian aa??ii?a,
ciaeaeaii ni?aa?aeiioaiiy, yea ia? oi/i?noue 0.07 % (ni?aa?aeiioaiiy
Aae-Iaia—Ieoai, ye a?aeiii, ia? oi/i?noue 0.58 %). A oeueiio i?aeoiae?
? aaaeeeaei oa, ui ia?aiao? aeaoi?iaoe?? q «aei?noei» o?enoaaany ioeai
oe?eeii iaaiiai iie?iiia.

5. Ia i?eeeaae? aa??ii?a JP=1/2+ oa JP=3/2+ iieacaii, ui aeei?enoaiiy
eaaioiaeo aeaaa? a ?ie? aeaaa? a?iiaoiai? neiao??? aoaeoeaii i?eaiaeeoue
aei a?aooaaiiy iae?i?eieo (iaiie?iii?aeueieo) aeeaae?a ii ii?ooaiith
oi?oa?ii? SU(3)-neiao???. Aeaii ii??aiyiiy ?iceeaaeo Ieoai (iiaiiai
?iceeaaeo ii ii?ooaiith SU(3)) c ia?oei ii?yaeeii ii ii?ooaiith
Uq(su(3)), ?iceeaaeaiiio ii ia?aiao?o h (q=eh) a ieie? h=0 («a ieie?»
eeane/ii? su3). Iieacaii, ui oe? aeaa ?iceeaaee oi/a ? ia ni?aiaaeathoue
oioiaeiuei, aea ? ocaiaeaeaieie.

6. Iiaoaeiaaii ianiaee iia?aoi?, yeee (c oi/ee ci?o eiai oaici?ieo
aeanoeainoae) ? oi/iei q—aiaeiaii eeane/iiai ianiaiai iia?aoi?a.
Ci?aa?aeiioaiiy aeey ian aa??ii?a c ieoaoo, yea io?eio?oueny i?e
aeei?enoaii? oeueiai ianiaiai iia?aoi?a, ia? cian?i i?inoee aeaeyae ?,
e??i oiai, ia? aeanoea?noue oi?aa?naeueiino? (iacaeaaei?noue a?ae aeai?o
i?aaenoaaeaiiy aeaaa?e aeeiai?/ii? neiao???). C ?ioiai aieo, aeey
oeueiai ni?aa?aeiioaiiy iaia? ?ioi? i?ioeaaeo?e o?enaoe?? ia?aiao?a
aeaoi?iaoe??, e??i i?ioeaaeo?e «i?aeaiiee».

7. Iieacaii, ui aeei?enoaiiy niaoe?aeueii neiino?oeiaaieo
‘eaac?ai?iiieo’ iia?aoi??a aea? ciiao iiaoaeoaaoe ?aae?caoe?th
aaaaoiia?aiao?e/ii? aeaoi?iaoe?? Uq;s(1),s(2),…,s(n-1)(gl(n)) aeaaa?e
E? gl(n). Aeiaeaoeia? ia?aiao?e aeaoi?iaoe?? s(1),s(2),…,s(n-1) yaii
aoiaeyoue a ia?anoaiiai/i? ni?aa?aeiioaiiy aeey eaac?ai?iiieo iia?aoi??a
??cieo ni?o?a.

8. Iiaoaeiaaii noaie o oie?anueeiio i?inoi?? ai?iiieo caoaeaeaiue, ui
a?aeiia?aeathoue aaeoi?iei iaciiai oa aa??iiai JP=3/2+. Ia iniia?
aeei?enoaiiy ianiaiai iia?aoi?a a ai?iii?e ?aae?caoe?? ciaeaeaii iania?
ni?aa?aeiioaiiy aeey oeeo aae?ii?a. Aiie ni?aiaee c io?eiaieie ?ai?oa o
oi?iae?ci? Aaeueoaiaea—Oeaoe?ia. Oei naiei aeiaaaeaii canoiniai?noue
ai?iiieo ?aae?caoe?e eaaioiaeo oi?oa?ieo aeaaa? aei io?eiaiiy ianiaeo
ni?aa?aeiioaiue aeey aae?ii?a; oea iiaea aeyaeoeny ei?eniei i?e
ia?aoiae? a?ae /enoi oaiiiaiieia?/ii? iiaeae?, ui aoea iienaia a
i?ae?icae?e? 2.2 aeena?oaoe??, aei a?eueo iine?aeiaii?
eaaioiai—iieueiai? iiaeae?.

NIENIE IIOAE?EIAAIEO I?AOeUe

CA OAIITH AeENA?OAOe??

1. Gavrilik A.M., Iorgov N.Z. Multiparameter deformations of gl(n)
algebra in terms of anyonic oscillators // J. Nonlin. Math. Phys. —
1996. — V. 3. — P.426-431.

2. Gavrilik A.M., Iorgov N.Z. q-deformed algebras Uq(son) and their
representations // Methods of Funct. Anal. and Topology. — 1997. — V. 3.
— N 4.- P.51-63.

3. Gavrilik A.M., Iorgov N.Z. Representations of the nonstandard
algebras Uq(so(n)) and Uq(so(n-1,1)) in Gel’fand—Tsetlin basis // Oe?.
O?c. AEo?i. — 1998. — O. 43. — N.791-797.

4. Gavrilik A.M., Iorgov N.Z. Quantum groups as flavor symmetries:
account of nonpolynomial SU(3)-breaking effects in ba ryon masses// Oe?.
O?c. AEo?i. — 1998. — O. 43. N.1526-1533.

5. A?ica A.A., ?i?aia I.C., Ee?iee A.O. I?i i?aaenoaaeaiiy eaaioiai?
aeaaa?e Uq(un,1) // Aeiiia?ae? IAI Oe?a?ie. — 1999. — N 2. — N.91-95.

6. Gavrilik A.M., Iorgov N.Z. q-Deformed inhomogeneous algebras Uq(ison)
and their representations // Proc. Int. Conf. Symmetry in Nonlinear
Mathematical Physics II. — Kiev. — 1997. — V. 2. — P.384-392.

7. Gavrilik A.M., Iorgov N.Z. Nonstandard q-deformation of the Euclidean
algebras and their representations // Proc. Int. Conf. Non-Euclidean
geometry in modern physics. — Uzhgorod. — 1997. — P.56-63.

8. Gavrilik A.M., Iorgov N.Z., Klimyk A.U. Nonstandard deformation
U’q(son): the imbedding U’q(son) Uq(sln) and representations // Proc.
Int. Conf. Symmetries in Science X (Bregenz, Austria, 1997).- New York:
Plenum. — 1998. — P. 121-133.

?i?aia I.C. I?aaenoaaeaiiy eaaioiaeo aeaaa? o?ce/ieo neiao??e oa ?o
canoinoaaiiy aei iieno ian aae?ii?a. — ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.04.02 — oai?aoe/ia
o?ceea. — ?inoeooo oai?aoe/ii? o?ceee IAI Oe?a?ie, Ee?a, 1999.

A aeena?oaoe?? aea/athoueny i?aaenoaaeaiiy q-aeaoi?iiaaieo aiaeia?a
U’q(son), Uq(ison) oa Uq(un,1) aeaaa? E? a?oi iaa?oaiue, aaee?aeiaeo oa
inaaaeioi?oa?ieo a?oi; oa aea?oueny ?o canoinoaaiiy. Aeey aeaaa?
U’q(son), Uq(ison) (n>5) aeiaaaeaii oai?aio i?i iaca?aei? i?aaenoaaeaiiy
(a aacen? Aaeueoaiaea—Oeaoe?ia). Ciaeaeaii aeaiaioe Eacei??a aeey
aeaaa? U’q(son), n=4,5,6. Eaaioia? aeaaa?e Uq(un) oa Uq(un,1)
canoiniaaii aei ciaoiaeaeaiiy iiaeo ianiaeo ni?aa?aeiioaiue (a?eueo
oi/ieo, i?ae ni?aa?aeiioaiiy Aae-Iaia—Ieoai) aeey aa??ii?a 1/2+.
Iieacaii, ui aeei?enoaiiy eaaioiaeo aeaaa? aeey iieno a?iiaoiai?
neiao??? aae?ii?a a?aoiao? iae?i?ei? aeeaaee ii ii?ooaiith
SU(3)-neiao???. A ai?iii?e ?aae?caoe?? Uq(sun) iiaoaeiaaii aaeoi?e
noai?a aeey iacii?a 1- oa aa??ii?a 3/2+ ? io?eiaii i?aaeea noi aeey ?o
ian.

Eeth/ia? neiaa: eaaioia? (q-aeaoi?iiaai?) aeaaa?e, i?aaenoaaeaiiy
aeaaa?, aeaaa?e aeeiai?/ii? neiao???, a?iiaoiaa neiao??y, aae?iie,
i?aaeea noi aeey ian, ai?iie.

Iorgov N.Z. Representations of quantum algebras of physical symmetries
and their application for treatment of hadron masses. — Manuscript.

Thesis for a candidate’s degree by speciality 01.04.02 — theoretical
physics. — Bogolyubov Institute for Theoretical Physics of National
Academy of Sciences of Ukraine, Kyiv, 1999.

In the thesis, representations of q-deformed analogs U’q(son), Uq(ison)
and Uq(un,1) of Lie algebras of rotation, Euclidean and pseudounitary
groups are explored, along with their applications.For the algebras
U’q(son), Uq(ison) (n>5), a theorem on irreducible representations (in
Gel’fand—Tsetlin basis) is proved. Basis Casimir elements for the
algebra U’q(son), n=4,5,6, are found. Quantum algebras Uq(un) and
Uq(un,1) are used to derive new mass relations (more accurate than the
Gell-Mann—Okubo one) for baryons 1/2+.It is shown, that usage of
quantum algebras as describing flavorsymmetries of hadrons accounts for
nonlinear contributions in SU(3)-breaking. Within anyonic realization of
Uq(sun), the state vectors for mesons 1- and baryons 3/2+ are
constructed, and mass sum rules obtained.

Key words: quantum (q-deformed) algebras, representations of algebras,
algebras of dynamical symmetry, flavor symmetry, hadrons, sum rules for
masses, anyons.

Ei?aia I.C. I?aaenoaaeaiea eaaioiauo aeaaa? oece/aneeo neiiao?ee e eo
i?eeiaeaiea e iienaieth iann aae?iiia. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.04.02 — oai?aoe/aneay
oeceea. — Einoeooo oai?aoe/aneie oeceee IAI Oe?aeiu, Eeaa, 1999.

Aeena?oaoeey iinayuaia eco/aieth i?aaenoaaeaiee q-aeaoi?ie?iaaiiuo
aeaaa? U’q(son), Uq(ison), Uq(un,1) aeaaa? Ee, niioaaonoaaiii, a?oii
a?auaiee, yaeeeaeiauo e inaaaeioieoa?iuo a?oii, e eo i?eeiaeaiee.

Aeey aeaaa? U’q(son) e Uq(ison), eioi?ua yaeythony ianoaiaea?oiuie
q-aeaoi?iaoeeyie aeaaa? Ee, niioaaonoaaiii, a?oiiu a?auaiee e a?oiiu
aeaeaeaiee n-ia?iiai i?ino?ainoaa, i?e n>5 aeaii aeieacaoaeuenoai oiai,
/oi iia?aoi?u, iieo/aaiua eaaceieieiaeueiie aeaoi?iaoeeae iia?aoi?ia
eeanne/aneeo i?aaenoaaeaiee a aacena Aaeueoaiaea—Oeaoeeia,
aeaenoaeoaeueii caaeatho i?aaenoaaeaiey yoeo q-aeaaa?. Yoio ?acoeueoao
anoue aua iaeiei iioaa?aeaeaieai i?eaiaeiinoe q-aiaeiaa oi?iaeecia
Aaeueoaiaea—Oeaoeeia aeey iino?iaiey i?aaenoaaeaiee q-aeaoi?ie?iaaiiuo
aeaaa?.

Aeey aeaaa? U’q(son), n=4,5,6, a yaiii aeaea iieo/aiu yeaiaiou Eaceie?a
aunoeo ii?yaeeia. A neo/aa aeaaa?u U’q(so4) iaeaeaiu nianoaaiiua
cia/aiey iia?aoi?ia Eaceie?a.

Aeaii aeieacaoaeuenoai oiai, /oi q-aiaeia iniiaiie iaoieoa?iie na?ee
caaeaao i?aaenoaaeaiey eaaioiaie aeaaa?u Uq(un,1). Yoi iicaieeei iaeoe
iai?eaiaeeiua e *-i?aaenoaaeaiey eaaioiaie aeaaa?u Uq(un,1).

Ia iniiaa eeanneoeeaoeee i?aaenoaaeaiee aeaaa? Uq(u4,1) e Uq(u5) iieo/ai
?yae iiauo ianniauo niioiioaiee aeey aa?eiiia JP=1/2+, eioi?ua yaeythony
q—aiaeiaaie ianniaiai niioiioaiey Aaee—Iaiia e Ieoai. N?aaee ieo
iaeaeaii niioiioaiea, eioi?ia i?e iiaenoaiiaea yiie?e/aneeo aeaiiuo aeey
iann aa?eiiia eiaao oi/iinoue 0.07 % (aeey n?aaiaiey, ecaanoiia
niioiioaiea Aaee-Iaiia—Ieoai eiaao oi/iinoue 0.58 %). A yoii iiaeoiaea
aaaeiui anoue oi, /oi ia?aiao? aeaoi?iaoeee q «aeanoei» oeene?iaaeny
ioeai aiieia ii?aaeaeaiiiai iieeiiia.

Ia i?eia?a aa?eiiia JP=1/2+ e JP=3/2+ iieacaii, /oi eniieueciaaiea
eaaioiauo aeaaa? a ?iee aeaaa? a?iiaoiaie neiiao?ee yooaeoeaii i?eaiaeeo
e o/aoo iaeeiaeiuo (iaiieeiiieaeueieo) aeeaaeia ii ia?ooaieth oieoa?iie
SU(3)-neiiao?ee. Aeaii n?aaiaiea ?aceiaeaiey Ieoai (iieiiai ?aceiaeaiey
ii ia?ooaieth SU(3)) n ia?aui ii?yaeeii ii ia?ooaieth Uq(su3),
?aceiaeaiiiio ii ia?aiao?o h (q=eh) a ie?anoiinoe h=0 («a ie?anoiinoe»
eeanne/aneie su3. Iieacaii, /oi yoe aeaa ?aceiaeaiey niaeaniaaiu, oioy e
ia niaiaaeatho oiaeaeanoaaiii.

Iino?iai ianniaue iia?aoi?, eioi?ue (n oi/ee c?aiey aai oaici?iuo
naienoa) anoue oi/iue q—aiaeia eeanne/aneiai ianniaiai iia?aoi?a.
Iieo/athueany i?e yoii niioiioaiey aeey iann aa?eiiia ec ieoaoa, eiatho
nianai i?inoie aeae e, e?iia oiai, eiatho naienoai oieaa?naeueiinoe
(iacaaeneiinoue io auai?a i?aaenoaaeaiey aeaaa?u aeeiaie/aneie
neiiao?ee). N ae?oaie noi?iiu, aeey yoiai niioiioaiey iao eiie
i?ioeaaeo?u oeenaoeee ia?aiao?a aeaoi?iaoeee, e?iia i?ioeaaeo?u
«iiaeaiiee».

Iieacaii, /oi eniieueciaaiea niaoeeaeueii neiino?oe?iaaiiuo
‘eaaceyieiiiuo’ iia?aoi?ia aeaao aiciiaeiinoue iino?ieoue ?aaeecaoeeth
iiiaiia?aiao?e/aneie aeaoi?iaoeee Uq;s_1,s_2,…,s_n-1(gln) aeaaa?u Ee
gln. Aeiiieieoaeueiua ia?aiao?u aeaoi?iaoeee s1,s2,…,sn-1 yaii aoiaeyo
a ia?anoaiiai/iua niioiioaiey aeey eaaceyieiiiuo iia?aoi?ia ?aciuo
ni?oia.

Iino?iaiu ninoiyiey a oieianeii i?ino?ainoaa yieiiiuo aicaoaeaeaiee,
eioi?ua niioaaonoaotho aaeoi?iui iaciiai e aa?eiiai JP=3/2+. I?e
eniieueciaaiee ianniaiai iia?aoi?a a yieiiiie ?aaeecaoeee iieo/aiu
niioiioaiey aeey iann yoeo aae?iiia. Iie niaiaee c iieo/aiiuie ?aiueoa a
oi?iaeecia Aaeueoaiaea—Oeaoeeia. Oai naiui aeieacaii i?eaiaeiinoue
yieiiiuo ?aaeecaoeee eaaioiauo oieoa?iuo aeaaa? aeey iieo/aiey
niioiioaiee aeey iann aae?iiia; yoi iiaeao ieacaoueny iieaciui i?e
ia?aoiaea io /enoi oaiiiaiieiae/aneie iiaeaee, eioi?ay eniieueciaaeanue
a aeenna?oaoeee, e aieaa iineaaeiaaoaeueiie eaaioiai—iieaaie iiaeaee.

Eeth/aaua neiaa: eaaioiaua (q-aeaoi?ie?iaaiiua) aeaaa?u, i?aaenoaaeaiey
aeaaa?, aeaaa?u aeeiaie/aneie neiiao?ee, a?iiaoiaay neiiao?ey, aae?iiu,
i?aaeea noii aeey iann, yieiiu.

?i?aia Ieeiea C?iia?eiae/

I?aaenoaaeaiiy eaaioiaeo aeaaa? o?ce/ieo neiao??e oa ?o canoinoaaiiy aei
iieno ian aae?ii?a.

(Aaoi?aoa?ao aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa

o?ceei-iaoaiaoe/ieo iaoe.)

Cai.- 27 Oi?iao 60 90 / 16
Iae.-aeae.a?e.- 1.0

I?aeienaii aei ae?oeo 1 eeiiy 1999 ?.
Oe?aae 100 i?ei.

Iie?a?ao?/ia ae?eueieoey ?OO ?i. I.I. Aiaiethaiaa IAI Oe?a?ie.

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