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 -disk polynomials. These are polynomials in two non-commuting variables which are expressed through little -Jacobi polynomials and that appear, for the value , as zonal spherical functions on a quantum analogue of the homogeneous space . This fact was first proved in [NYM] (see also [Fl]). In a previous paper [Fl] we proved an addition formula for these -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].
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}
}