On Algebraically Integrable Differential Operators on an Elliptic Curve

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dc.contributor.authorEtingof, P.
dc.contributor.authorRains, E.
dc.date.accessioned2019-02-13T18:07:21Z
dc.date.available2019-02-13T18:07:21Z
dc.date.issued2011
dc.description.abstractWe 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.sponsorshipThis 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.identifier.citationOn 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.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 35J35; 70H06
dc.identifier.otherDOI:10.3842/SIGMA.2011.062
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/147170
dc.language.isoenuk_UA
dc.publisherІнститут математики НАН Україниuk_UA
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlieruk_UA
dc.titleOn Algebraically Integrable Differential Operators on an Elliptic Curveuk_UA
dc.typeArticleuk_UA

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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік