English

A non-commutative discrete hypergroup associated with q-disk polynomials

Quantum Algebra 2016-09-06 v1 Classical Analysis and ODEs

Abstract

The aim of this paper is to give an example of a non-commutative discrete hypergroup associated with qq-disk polynomials. These are polynomials Rl,m(\a)R_{l,m}^{(\a)} in two non-commuting variables which are expressed through little qq-Jacobi polynomials and that appear, for the value \a=n2\a=n-2, as zonal spherical functions on a quantum analogue of the homogeneous space U(n)/U(n1)U(n)/U(n-1). This fact was first proved in [NYM] (see also [Fl]). In a previous paper [Fl] we proved an addition formula for these qq-disk polynomials. It is this addition formula that will allow us to prove positivity of linearization coefficients in a manner similar to [Koo1], and to construct from it a DJS-hypergroup following [Koo4].

Keywords

Cite

@article{arxiv.math/9411230,
  title  = {A non-commutative discrete hypergroup associated with q-disk polynomials},
  author = {Paul G. A. Floris},
  journal= {arXiv preprint arXiv:math/9411230},
  year   = {2016}
}