Limits of Gaudin Systems: Classical and Quantum Cases
We consider the XXX homogeneous Gaudin system with N sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals (in the classical case) and new '...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
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| Sprache: | English |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149175 |
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| Zitieren: | Limits of Gaudin Systems: Classical and Quantum Cases / A. Chervov, G. Falqui, L. Rybnikov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 34 назв. — англ. |
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Chervov, A. Falqui, G. Rybnikov, L. 2019-02-19T18:12:49Z 2019-02-19T18:12:49Z 2009 Limits of Gaudin Systems: Classical and Quantum Cases / A. Chervov, G. Falqui, L. Rybnikov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 34 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 82B23; 81R12; 17B80; 81R50 https://nasplib.isofts.kiev.ua/handle/123456789/149175 We consider the XXX homogeneous Gaudin system with N sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals (in the classical case) and new ''Gaudin'' algebras (in the quantum case). We will especially treat the case of total collisions, that gives rise to (a generalization of) the so called Bending flows of Kapovich and Millson. Some aspects of multi-Poisson geometry will be addressed (in the classical case). We will make use of properties of ''Manin matrices'' to provide explicit generators of the Gaudin Algebras in the quantum case. This paper is a contribution to the Proceedings of the XVIIth International Colloquium on Integrable Systems and Quantum Symmetries (June 19–22, 2008, Prague, Czech Republic). G.F. acknowledges support from the ESF programme MISGAM, and the Marie Curie RTN ENIGMA. The work of A.C. and L.R. has been partially supported by the Russian Federal Nuclear Energy Agency. A.C. has been partially supported by the Russian President Grant MK-5056.2007.1, by the grant of Support for the Scientific Schools 3035.2008.2, by the RFBR grant 08-02-00287a, and by the ANR grant GIMP (Geometry and Integrability in Mathematics and Physics). The work of L.R. was partially supported by the RFBR grant 05 01 00988-a and the RFBR grants 05-01-02805-CNRSL-a and 07-01-92214-CNRSL-a. Also, L.R. gratefully acknowledges the support from the Deligne 2004 Balzan prize in mathematics. We thank the referees for useful remarks. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Limits of Gaudin Systems: Classical and Quantum Cases Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Limits of Gaudin Systems: Classical and Quantum Cases |
| spellingShingle |
Limits of Gaudin Systems: Classical and Quantum Cases Chervov, A. Falqui, G. Rybnikov, L. |
| title_short |
Limits of Gaudin Systems: Classical and Quantum Cases |
| title_full |
Limits of Gaudin Systems: Classical and Quantum Cases |
| title_fullStr |
Limits of Gaudin Systems: Classical and Quantum Cases |
| title_full_unstemmed |
Limits of Gaudin Systems: Classical and Quantum Cases |
| title_sort |
limits of gaudin systems: classical and quantum cases |
| author |
Chervov, A. Falqui, G. Rybnikov, L. |
| author_facet |
Chervov, A. Falqui, G. Rybnikov, L. |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We consider the XXX homogeneous Gaudin system with N sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals (in the classical case) and new ''Gaudin'' algebras (in the quantum case). We will especially treat the case of total collisions, that gives rise to (a generalization of) the so called Bending flows of Kapovich and Millson. Some aspects of multi-Poisson geometry will be addressed (in the classical case). We will make use of properties of ''Manin matrices'' to provide explicit generators of the Gaudin Algebras in the quantum case.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149175 |
| citation_txt |
Limits of Gaudin Systems: Classical and Quantum Cases / A. Chervov, G. Falqui, L. Rybnikov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 34 назв. — англ. |
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AT chervova limitsofgaudinsystemsclassicalandquantumcases AT falquig limitsofgaudinsystemsclassicalandquantumcases AT rybnikovl limitsofgaudinsystemsclassicalandquantumcases |
| first_indexed |
2025-12-07T19:03:32Z |
| last_indexed |
2025-12-07T19:03:32Z |
| _version_ |
1850877371561803776 |