Limits of Gaudin Systems: Classical and Quantum Cases

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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dc.contributor.author	Chervov, A.
dc.contributor.author	Falqui, G.
dc.contributor.author	Rybnikov, L.
dc.date.accessioned	2019-02-19T18:12:49Z
dc.date.available	2019-02-19T18:12:49Z
dc.date.issued	2009
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2000 Mathematics Subject Classification: 82B23; 81R12; 17B80; 81R50
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149175
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Limits of Gaudin Systems: Classical and Quantum Cases	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA