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Discretization of Baker-Akhiezer modules and commuting difference operators in several discrete variables


Authors: Andrey Mironov and Atsushi Nakayashiki
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 74 (2013), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2013, 261-279
Published electronically: April 9, 2014
MathSciNet review: 3235800
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Abstract | References | Additional Information

Abstract: We introduce the notion of discrete Baker-Akhiezer (DBA) modules, which are modules over the ring of difference operators, as a discretization of Baker-Akhiezer modules, which are modules over the ring of differential operators. We use it to construct commuting difference operators with matrix coefficients in several discrete variables.


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Additional Information

Andrey Mironov
Affiliation: Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia — and — Laboratory of Geometric Methods in Mathematical Physics, Moscow State University
Email: mironov@math.nsc.ru

Atsushi Nakayashiki
Affiliation: Department of Mathematics, Tsuda College, Kodaira, Tokyo, Japan
Email: atsushi@tsuda.ac.jp

DOI: https://doi.org/10.1090/S0077-1554-2014-00219-3
Published electronically: April 9, 2014
Dedicated: Dedicated to Viktor Matveevich Buchstaber on his seventieth birthday
Article copyright: © Copyright 2014 American Mathematical Society