Harmonic analysis of boxed hyperoctahedral Hall-Littlewood polynomials

Diejen, J. F. van

doi:10.1016/j.jfa.2021.109256

Cited by 2 publications

(1 citation statement)

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“…It is hard to overstate the role that the classical orthogonal polynomials have played in mathematics and physics over the last few centuries. Recently, there have been interesting multivariate extensions of this theory based on connections with quantum integrable systems, representation theory and algebraic combinatorics, see for instance [3,4,5,7,11,28,31] and the references therein. In particular, the work [25] describing the irreducible representations of the symmetry algebra of the generic superintegrable system on the 3-sphere suggested that spectral properties of multivariate extensions of the classical orthogonal polynomials were intimately related to first integrals of superintegrable systems.…”

Section: Introductionmentioning

confidence: 99%

Gaudin model for the multinomial distribution

Илиев¹

2023

Preprint

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The goal of the paper is to analyze a Gaudin model for a polynomial representation of the Kohno-Drinfeld Lie algebra associated with the multinomial distribution. The main result is the construction of an explicit basis of the space of polynomials consisting of common eigenfunctions of Gaudin operators in terms of Aomoto-Gelfand hypergeometric series. The construction shows that the polynomials in this basis are also common eigenfunctions of the operators for a dual Gaudin model acting on the degree indices, and therefore they provide a solution to a multivariate discrete bispectral problem.

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