Huge formulas for simple special functions
Seminar Room 1, Newton Institute
We recall some simple special functions of basic hypergeometric type, amongst others the q-Laguerre polynomials, q-Bessel functions and 2phi1-series. In the GNS-representation for the Haar weight for the quantum group analogue of the normaliser of SU(1,1) in SL(2,C) such functions occur as the matrix coefficients of the multiplicative unitary, and for this reason these functions occur as coefficients in certain expansions in the dual quantum group. The purpose of the talk is to show how such interpretations give rise to huge formulas for these functions, including big expansion formulas and some positivity results. These results are actually spin-off from the study of the dual quantum group, which is joint work with Wolter Groenevelt (Delft) and Johan Kustermans (Leuven).