Published July 7, 2011
| Submitted + Published
Journal Article
Open
On Algebraically Integrable Differential Operators on an Elliptic Curve
- Creators
- Etingof, Pavel
-
Rains, Eric
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).
Additional Information
© 2011 Institute of Mathematics of National Academy of Sciences of Ukraine. Received April 25, 2011, in final form June 30, 2011; Published online July 07, 2011. 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.Attached Files
Published - Etingof2011p15152Symmetry_Integr_Geom.pdf
Submitted - 1011.6410.pdf
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Additional details
- Eprint ID
- 24528
- Resolver ID
- CaltechAUTHORS:20110725-113214387
- DMS-0504847
- NSF
- DMS-0854764
- NSF
- DMS-1001645
- NSF
- Created
-
2011-07-25Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field