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Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence

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posted on 19.04.2021, 11:01 by Misha Feigin, Martin Hallnas, Alexander VeselovAlexander Veselov
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 quasiinvariant 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-quasiinvariants, 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.

Funding

Swedish Research Council (Reg. nr. 2018-04291)

Russian Science Foundation grant no. 20-11-20214

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Communications in Mathematical Physics

Volume

386

Issue

1

Pages

107-141

Publisher

Springer (part of Springer Nature)

Version

VoR (Version of Record)

Rights holder

© The Authors

Publisher statement

This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/

Acceptance date

05/02/2021

Publication date

2021-03-15

Copyright date

2021

ISSN

0010-3616

eISSN

1432-0916

Language

en

Depositor

Prof Alexander Veselov . Deposit date: 4 February 2021

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