Glasgow Mathematical Journal

Table of Contents - 2009 - Volume 51, Issue A  

Research Article

TRIGONOMETRIC DARBOUX TRANSFORMATIONS AND CALOGERO–MOSER MATRICES

LUC HAINEa1, EMIL HOROZOVa2 and PLAMEN ILIEVa3

a1 Department of Mathematics, Université catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium e-mail: luc.haine@uclouvain.be

a2 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

a3 School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332–0160, USA e-mail: iliev@math.gatech.edu

Abstract

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.

2000 Mathematics Subject Classification

  • 35Q53;
  • 37K10