Treffer: A noncommutative discrete hypergroup associated with q-disk polynomials: A noncommutative discrete hypergroup associated with \(q\)-disk polynomials

Title:
A noncommutative discrete hypergroup associated with q-disk polynomials: A noncommutative discrete hypergroup associated with \(q\)-disk polynomials
Authors:
Paul G. A. Floris
Source:
Journal of Computational and Applied Mathematics. 68:69-78
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 1996.
Publication Year:
1996
Subject Terms:
DJS-hypergroup, Applied Mathematics, Other basic hypergeometric functions and integrals in several variables, Quantum groups (quantized enveloping algebras) and related deformations, non-commutative hypergroup structure, 01 natural sciences, q-Disk polynomials, Computational Mathematics, Linearization coefficients, Mathematics - Classical Analysis and ODEs, compact quantum Gelfand pairs, Mathematics - Quantum Algebra, hypergroups, Classical Analysis and ODEs (math.CA), FOS: Mathematics, nonnegativity of the linearization coefficients, Quantum Algebra (math.QA), 0101 mathematics, Harmonic analysis on hypergroups, \(q\)-disk polynomials
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
0377-0427
DOI:
10.1016/0377-0427(95)00256-1
DOI:
10.48550/arxiv.math/9411230
Access URL:
http://arxiv.org/abs/math/9411230
https://core.ac.uk/display/82257811
https://www.sciencedirect.com/science/article/abs/pii/0377042795002561
https://www.sciencedirect.com/science/article/pii/0377042795002561
https://ui.adsabs.harvard.edu/abs/1994math.....11230F/abstract
Rights:
Elsevier Non-Commercial
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....b91dba587bde1bddda1d4dd2a5dc46f6
Database:
OpenAIRE

Weitere Informationen

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].