Abstract
AbstractLassalle and Nekrasov discovered in the 1990s a surprising correspondence between the rational Calogero–Moser system with a harmonic term and its trigonometric version. We present a conceptual explanation of this correspondence using the rational Cherednik algebra and establish its quasi-invariant extension. More specifically, we consider configurations $${\mathcal {A}}$$
A
of real hyperplanes with multiplicities admitting the rational Baker–Akhiezer function and use this to introduce a new class of non-symmetric polynomials, which we call $${\mathcal {A}}$$
A
-Hermite polynomials. These polynomials form a linear basis in the space of $${\mathcal {A}}$$
A
-quasi-invariants, which is an eigenbasis for the corresponding generalised rational Calogero–Moser operator with harmonic term. In the case of the Coxeter configuration of type $$A_N$$
A
N
this leads to a quasi-invariant version of the Lassalle–Nekrasov correspondence and its higher order analogues.
Funder
Vetenskapsrådet
Russian Science Foundation
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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