Feigin2021_Article_QuasiInvariantHermitePolynomia.pdf (522.53 kB)
Download fileQuasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence
journal contribution
posted on 2021-04-19, 11:01 authored by Misha Feigin, Martin Hallnas, Alexander VeselovAlexander VeselovLassalle 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 PhysicsVolume
386Issue
1Pages
107-141Publisher
Springer (part of Springer Nature)Version
- VoR (Version of Record)
Rights holder
© The AuthorsPublisher 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
2021-02-05Publication date
2021-03-15Copyright date
2021ISSN
0010-3616eISSN
1432-0916Publisher version
Language
- en