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