Eight lectures on quantum groups and q-special functions

Abstract

The lectures contain an introduction to quantum groups, q-special functions and their interplay. After generalities on Hopf algebras, ortogonal polynomials and basic hypergeometric series we work out the relation between the quantum SU(2) group and the Askey-Wilson polynomials out in detail as the main example. As an application we derive an addition formula for a two-parameter subfamily of Askey-Wilson polynomials. A relation between the AISalam and Chihara polynomials and the quantised universal enveloping algebra for sυ(1, 1) is given. Finally, more examples and other approaches as well as some open problems are given.