On Algebraically Integrable Differential Operators on an Elliptic Curve

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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dc.contributor.author	Etingof, P.
dc.contributor.author	Rains, E.
dc.date.accessioned	2019-02-13T18:07:21Z
dc.date.available	2019-02-13T18:07:21Z
dc.date.issued	2011
dc.identifier.citation	On Algebraically Integrable Differential Operators on an Elliptic Curve / P. Etingof, E. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 35J35; 70H06
dc.identifier.other	DOI:10.3842/SIGMA.2011.062
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147170
dc.description.abstract	We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special elliptic curves defined over Q which do not deform to generic elliptic curves. We also study algebraically integrable operators of higher order with several poles and with symmetries, and (conjecturally) relate them to crystallographic elliptic Calogero-Moser systems (which is a generalization of the results of Airault, McKean, and Moser).	uk_UA
dc.description.sponsorship	This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/OPSF.html. The authors are grateful to I. Krichever, E. Previato, and A. Veselov for useful discussions. The work of P.E. was partially supported by the the NSF grants DMS-0504847 and DMS-0854764. The work of E.R. was partially supported by the NSF grant DMS-1001645.	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	On Algebraically Integrable Differential Operators on an Elliptic Curve	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA