Trigonometric Darboux transformations and Calogero-Moser matrices
Luc Haine, Emil Horozov, Plamen Iliev
TL;DR
This paper characterizes certain rational Grassmannian spaces via Darboux transformations, linking them to trigonometric Calogero-Moser matrices and resulting in commutative rings of differential operators with rational exponential coefficients.
Contribution
It introduces a novel characterization of Segal-Wilson rational Grassmannian subspaces using Darboux transformations and parametrizes them with trigonometric Calogero-Moser matrices.
Findings
Identifies a correspondence between Darboux transformations and rational Grassmannian spaces.
Establishes a parametrization of these spaces using trigonometric Calogero-Moser matrices.
Describes the structure of commutative rings of differential operators with exponential rational coefficients.
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.
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