This paper introduces a family of Askey-Wilson type orthogonal polynomials in n variables associated with a root system of type BCn. The family depends, apart from q, on 5 parameters. For n = 1 itâ€¦ (More)

We generalise the quantum double construction of Drinfelâ€™d to the case of the (Hopf) algebra of suitable functions on a compact or locally compact group. We will concentrate on the âˆ—-algebraâ€¦ (More)

Recently the author derived a Laplace integral representation, a product formula and an addition formula for Jacobi polynomials Ppfi). The results are (1) (2) and (3) * j, ,I " (~0~2 0-f-2 sin2 0 +â€¦ (More)

The purely algebraic notion of CQG algebra (algebra of functions on a compact quantum group) is defined. In a straightforward algebraic manner, the Peter-Weyl theorem for CQG algebras and theâ€¦ (More)

On the SU(2) quantum group the notion of (zonal) spherical element is generalized by considering left and right invariance in the infinitesimal sense with respect to twisted primitive elements of theâ€¦ (More)

This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generallyâ€¦ (More)

Gosperâ€™s and Zeilbergerâ€™s algorithms for summation of terminating hypergeometric series as well as the q-versions of these algorithms are described in a very rigorous way. The paper is a companion toâ€¦ (More)

This is a survey of interpretations of q hypergeometric orthogonal polynomials on quantum groups The rst half of the paper gives general background on Hopf algebras and quantum groups The emphasis inâ€¦ (More)

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible âˆ—-representations.â€¦ (More)

For a quantum group G the notion of quantum homogeneous G-space is defined. Two methods to construct such spaces are discussed. The first one makes use of quantum subgroups, the second more generalâ€¦ (More)