Lassalle-Nekrasov correspondence for Calogero-Moser systems and quasi-invariant Hermite polynomials

Lassalle and Nekrasov observed in the 1990s relations between the rational Calogero-Moser system with harmonic term and the trigonometric Calogero-Moser system. In the quantum case this amounts to an operator on the algebra of symmetric polynomials which intertwines actions of corresponding quantum integrals of these two systems. I would like to explain this relation and its generalisations by making use of automorphisms of the rational Cherednik algebra. For integer coupling parameter the algebra of symmetric polynomials can be extended by quasi-invariants, which is a module for the spherical subalgebra of Cherednik algebra, and we get a class of non-symmetric polynomials which are eigenfunctions of the rational Hamiltonian. The talk is based on joint work with Martin Hallnäs and Alexander Veselov.