Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence

Feigin, M. V. , Hallnäs, M. A. and Veselov, A. P. (2021) Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence. Communications in Mathematical Physics, 386(1), pp. 107-141. (doi: 10.1007/s00220-021-04036-8)

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Feigin, Professor Misha
Authors: Feigin, M. V., Hallnäs, M. A., and Veselov, A. P.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Communications in Mathematical Physics
ISSN (Online):1432-0916
Published Online:15 March 2021
Copyright Holders:Copyright © 2021 The Authors
First Published:First published in Communications in Mathematical Physics 386(1): 107-141
Publisher Policy:Reproduced under a Creative Commons licence
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