On Algebraically Integrable Differential Operators on an Elliptic Curve

Author(s)
Etingof, Pavel I.; Rains, Eric
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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).
Description
Contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”
Date issued
2011-07
URI
http://hdl.handle.net/1721.1/71197
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Symmetry, Integrability and Geometry, Methods and Applications
Publisher
National Academy of Sciences of Ukraine
Citation
Etingof, Pavel. “On Algebraically Integrable Differential Operators on an Elliptic Curve.” Symmetry, Integrability and Geometry: Methods and Applications, SIGMA 7 (2011), 062, 19 pages. Web.
Version: Final published version
ISSN
1815-0659
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