Trigonometric Darboux transformations and Calogero-Moser matrices
arXiv:0807.2888 · doi:10.1017/S0017089508004813
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 e^x. The resulting subgrassmannian is parametrized in terms of trigonometric Calogero-Moser matrices.