Bethe algebra of Gaudin model, Calogero-Moser space and Cherednik algebra

TL;DR

This paper establishes a deep connection between the Bethe algebra of the Gaudin model, the center of the rational Cherednik algebra, and the algebra of functions on the Calogero-Moser space, revealing new algebraic insights.

Contribution

It identifies the Bethe algebra of the Gaudin model with the center of the rational Cherednik algebra and the functions on Calogero-Moser space, unifying these structures.

Findings

Bethe algebra is isomorphic to the center of the Cherednik algebra

Bethe algebra corresponds to functions on Calogero-Moser space

Provides new algebraic links between integrable models and geometric spaces

Abstract

We identify the Bethe algebra of the Gaudin model associated to gl(N) acting on a suitable representation with the center of the rational Cherednik algebra and with the algebra of regular functions on the Calogero-Moser space.