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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| Datum: | 2011 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2011
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147170 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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