Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence

Autor:	Feigin, M. V., Hallnäs, M. A., Veselov, A. P.
Rok vydání:	2020
Předmět:	Mathematical Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
DOI:	10.1007/s00220-021-04036-8
Popis:	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 $\mathcal A$ 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 $\mathcal A$-Hermite polynomials. These polynomials form a linear basis in the space of $\mathcal A$-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 $A_N$ this leads to a quasi-invariant version of the Lassalle-Nekrasov correspondence and its higher order analogues. Comment: 32 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2008.06010 Zobrazit plný text záznamu View this record from Arxiv