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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Abstract
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 |
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Status: | Published |
Refereed: | Yes |
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 |
Publisher: | Springer |
ISSN: | 0010-3616 |
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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