The lecture notes contains an introduction to quantum groups, q-special functions and their interplay. After generalities on Hopf algebras, orthogonal polynomials and basic hypergeometric series weâ€¦ (More)

In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform,â€¦ (More)

The decomposition of the tensor product of a positive and a negative discrete series representation of the Lie algebra su(1, 1) is a direct integral over the principal unitary series representations.â€¦ (More)

S.L. Woronowicz proved in 1991 that quantum SU(1,1) does not exist as a locally compact quantum group. Results by L.I. Korogodsky in 1994 and more recently by Woronowicz gave strong indications thatâ€¦ (More)

Dynamical quantum groups were recently introduced by Etingof and Varchenko as an algebraic framework for studying the dynamical Yangâ€“Baxter equation, which is precisely the Yangâ€“Baxter equationâ€¦ (More)

An explicit bilinear generating function for Meixner-Pollaczek polynomials is proved. This formula involves continuous dual Hahn polynomials, Meixner-Pollaczek functions, and non-polynomialâ€¦ (More)

Abstract. The Stieltjesâ€“Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider theâ€¦ (More)

The main goal is to interpret the Askey-Wilson function and the corresponding transform pair on the quantum SU(1, 1) group. A weight on the C *-algebra of continuous functions vanishing at infinityâ€¦ (More)

The q-Laguerre polynomials correspond to an indetermined moment problem. For explicit discrete non-N-extremal measures corresponding to Ramanujan's 1 Ïˆ 1-summation we complement the orthogonalâ€¦ (More)