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

1994/11/29 by Floris, Paul G. A.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.math/9411230

Abstract

The aim of this paper is to give an example of a non-commutative discrete hypergroup associated with q-disk polynomials. These are polynomials R_l,m^(\a) in two non-commuting variables which are expressed through little q-Jacobi polynomials and that appear, for the value \a=n-2, as zonal spherical functions on a quantum analogue of the homogeneous space 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 q-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].

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