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TRIGONOMETRIC DARBOUX TRANSFORMATIONS AND CALOGERO–MOSER MATRICES

Published online by Cambridge University Press:  01 February 2009

LUC HAINE ,
EMIL HOROZOV  and
PLAMEN ILIEV
LUC HAINE
Affiliation:
Department of Mathematics, Université catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium e-mail: luc.haine@uclouvain.be
EMIL HOROZOV
Affiliation:
Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Boulevard, Sofia 1126, Bulgaria and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria e-mail: horozov@fmi.uni-sofia.bg
PLAMEN ILIEV
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332–0160, USA e-mail: iliev@math.gatech.edu
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Abstract

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We characterize in terms of Darboux transformations the spaces in the Segal–Wilson rational Grassmannian, which lead to commutative rings of differential operators having coefficients which are rational functions of ex. The resulting subgrassmannian is parametrized in terms of trigonometric Calogero–Moser matrices.

Keywords

35Q5337K10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue A , February 2009 , pp. 95 - 106
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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