R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain
The problem of constructing the SL(N,C) invariant solutions to the Yang-Baxter equation is considered. The solutions (R-operators) for arbitrarily principal series representations of SL(N,C) are obtained in an explicit form. We construct the commutative family of the operators Qk(u) which can be ide...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2006 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146069 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain / S.É. Derkachov, A.N. Manashov // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 39 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862607233945174016 |
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| author | Derkachov, S.É. Manashov, A.N. |
| author_facet | Derkachov, S.É. Manashov, A.N. |
| citation_txt | R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain / S.É. Derkachov, A.N. Manashov // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 39 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The problem of constructing the SL(N,C) invariant solutions to the Yang-Baxter equation is considered. The solutions (R-operators) for arbitrarily principal series representations of SL(N,C) are obtained in an explicit form. We construct the commutative family of the operators Qk(u) which can be identified with the Baxter operators for the noncompact SL(N,C) spin magnet.
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| first_indexed | 2025-11-28T13:55:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146069 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-28T13:55:30Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Derkachov, S.É. Manashov, A.N. 2019-02-06T17:26:34Z 2019-02-06T17:26:34Z 2006 R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain / S.É. Derkachov, A.N. Manashov // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 39 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 82B23; 82B20 https://nasplib.isofts.kiev.ua/handle/123456789/146069 The problem of constructing the SL(N,C) invariant solutions to the Yang-Baxter equation is considered. The solutions (R-operators) for arbitrarily principal series representations of SL(N,C) are obtained in an explicit form. We construct the commutative family of the operators Qk(u) which can be identified with the Baxter operators for the noncompact SL(N,C) spin magnet. This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. We are grateful to M.A. Semenov-Tian-Shansky for valuable discussions and attracting our attention to. This work was supported by the RFFI grant 05-01-00922 and DFG grant 436 Rus 17/9/06 (S.D.) and by the Helmholtz Association, contract number VH-NG-004 (A.M.) en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain Article published earlier |
| spellingShingle | R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain Derkachov, S.É. Manashov, A.N. |
| title | R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain |
| title_full | R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain |
| title_fullStr | R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain |
| title_full_unstemmed | R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain |
| title_short | R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain |
| title_sort | r-matrix and baxter q-operators for the noncompact sl(n,c) invariant spin chain |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146069 |
| work_keys_str_mv | AT derkachovse rmatrixandbaxterqoperatorsforthenoncompactslncinvariantspinchain AT manashovan rmatrixandbaxterqoperatorsforthenoncompactslncinvariantspinchain |