On Algebraically Integrable Differential Operators on an Elliptic Curve
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 gener...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147170 |
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| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147170 |
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Etingof, P. Rains, E. 2019-02-13T18:07:21Z 2019-02-13T18:07:21Z 2011 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. 1815-0659 2010 Mathematics Subject Classification: 35J35; 70H06 DOI:10.3842/SIGMA.2011.062 https://nasplib.isofts.kiev.ua/handle/123456789/147170 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). 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Algebraically Integrable Differential Operators on an Elliptic Curve Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On Algebraically Integrable Differential Operators on an Elliptic Curve |
| spellingShingle |
On Algebraically Integrable Differential Operators on an Elliptic Curve Etingof, P. Rains, E. |
| title_short |
On Algebraically Integrable Differential Operators on an Elliptic Curve |
| title_full |
On Algebraically Integrable Differential Operators on an Elliptic Curve |
| title_fullStr |
On Algebraically Integrable Differential Operators on an Elliptic Curve |
| title_full_unstemmed |
On Algebraically Integrable Differential Operators on an Elliptic Curve |
| title_sort |
on algebraically integrable differential operators on an elliptic curve |
| author |
Etingof, P. Rains, E. |
| author_facet |
Etingof, P. Rains, E. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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).
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147170 |
| citation_txt |
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. |
| work_keys_str_mv |
AT etingofp onalgebraicallyintegrabledifferentialoperatorsonanellipticcurve AT rainse onalgebraicallyintegrabledifferentialoperatorsonanellipticcurve |
| first_indexed |
2025-12-07T19:21:19Z |
| last_indexed |
2025-12-07T19:21:19Z |
| _version_ |
1850878491233353728 |