Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model

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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	Rubtsov, V.
dc.contributor.author	Silantyev, A.
dc.contributor.author	Talalaev, D.
dc.date.accessioned	2019-02-19T17:10:13Z
dc.date.available	2019-02-19T17:10:13Z
dc.date.issued	2009
dc.identifier.citation	Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model / V. Rubtsov, A. Silantyev, D. Talalaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	DOI:10.3842/SIGMA.2009.110
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149089
dc.description.abstract	In this paper we construct the quantum spectral curve for the quantum dynamical elliptic gln Gaudin model. We realize it considering a commutative family corresponding to the Felder's elliptic quantum group Eτ,h(gln) and taking the appropriate limit. The approach of Manin matrices here suits well to the problem of constructing the generation function of commuting elements which plays an important role in SoV and Langlands concept.	uk_UA
dc.description.sponsorship	This paper is a contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions” (July 21–25, 2008, MPIM, Bonn, Germany). The work of V.R. was partially supported by the RFBR grant 08-01-00667 and grant of Support for the Scientific Schools 3036.2008.2. V.R. is also grateful to French-Ukrainian PICS 2009. D.T. and A.S. would like to thank LAREMA and Mathematical Department of the University of Angers for the hospitality during the visits where the part of the work was done. The work of A.S. was partially supported by the EPSRC grant EP/F032889/1 and the RFBR grant 09-01-00239-a. This work of D.T. was partially supported by the Federal Nuclear Energy Agency of Russia, the RFBR grant 07-02-00645, the grant of Support for the Scientific Schools 3035.2008.2, and the fund “Dynasty”. V.R. and D.T. are thankful to the MATPYL Federation support of D.T. visit in Angers. V.R. and D.T. acknowledge the hospitality and an excellent working atmosphere during the International Workshop “Elliptic integrable systems, isomonodromy problems, and hypergeometric functions” in the Hausdorf f Centrum and Max-Planck-Institute for Mathematics in Bonn in July 2008. They are grateful to organizers for the invitation. A part of results was presented by V.R. in his talk during the MISGAM-SISSA International Conference “From integrable structures to topological strings and back” in September 2008. He is thankful to MISGAM and SISSA for this invitation and support. At last but not the least our thanks to anonymous referees for their careful reading and numerous useful remarks and suggestions.	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	Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA