Work

Cherednik Operators and Ruijsenaars–Schneider Model at Infinity

Year: 2017

Type: article

Abstract: Heckman introduced |$N$| operators on the space of polynomials in |$N$| variables, such that these operators form a covariant set relative to permutations of the operators and variables, and such that Jack symmetric polynomials are eigenfunctions of the power sums of these operators. We introduce the analogues of these |$N$| operators for Macdonald symmetric polynomials, by using Cherednik operators. The latter operators pairwise commute, and Macdonald polynomials are eigenfunctions of their power sums. We compute the limits of our operators at |$N\to\infty$|⁠. These limits yield a Lax operator for Macdonald symmetric functions.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnx176

Authors: Maxim Nazarov, Evgeny Sklyanin

Institution: University of York

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Awards: G220696261, G40982390, G8922700664