Trigonometric Darboux transformations and Calogero-Moser matrices
  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. 
Luc Haine, Emil Horozov, Plamen Iliev