Quasi-invariant Hermite Polynomials and Lassalle-Nekrasov Correspondence
Journal article, 2021

Lassalle 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 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 A-Hermite polynomials. These polynomials form a linear basis in the space of 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 AN this leads to a quasi-invariant version of the Lassalle-Nekrasov correspondence and its higher order analogues.

Author

Misha V. Feigin

Moscow State University

University of Glasgow

Martin Hallnäs

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Alexander P. Veselov

Russian Academy of Sciences

Moscow State University

Loughborough University

Communications in Mathematical Physics

0010-3616 (ISSN) 1432-0916 (eISSN)

Vol. 386 107-141

Quasi-invariants of finite Coxeter groups and integrable systems

Swedish Research Council (VR) (2018-04291), 2019-01-01 -- 2022-12-31.

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1007/s00220-021-04036-8

More information

Latest update

8/6/2021 7