On algebraically integrable differential operators on an elliptic curve
type: Item
instance of: scholarly article
title: On algebraically integrable differential operators on an elliptic curve
zbMATH Open document ID: 1247.37045
DOI: 10.3842/SIGMA.2011.062
published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
publication date: 2012-06-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1011.6410
review text: The authors give an exposition of the general theory of algebraically integrable operators (i.e., finite gap), in particular of those on elliptic curves; most of the results here are well known, but for the reader's convenience the authors give an exposition based on differential Galois theory and propose a general conjecture regarding the classification of operators with one pole. They present computational results for third order algebraically integrable operators with one pole and give a conjectural classification of such operators. Finally, algebraically integrable operators of higher order with several poles and with symmetries are studied and a conjecture on the connection with the crystallographic elliptic Calogero-Moser systems is stated which can be seen as a generalization of well-known results of Airault, McKean, and Moser.
reviewed by: Ahmed Lesfari
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 70H06
zbMATH DE Number: 6050681
zbMATH Keywords: finite gap differential operator
zbMATH Keywords: monodromy
zbMATH Keywords: elliptic Calogero-Moser system
Wikidata QID: Q115219670
author: Pavel Etingof
author: Eric Rains
MaRDI profile type: Publication
arXiv ID: 1011.6410
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description: scientific article; zbMATH DE number 6050681