Eight lectures on quantum groups and q - special functions
Erik Koelink Universiteit van Amsterdam, THE NETHERLANDS
Abstract.
The lectures contain an introduction to quantum groups, q - special functions and their interplay. After generalities on Hopf algebras, orthogonal polynomials and basic hypergeometric series we work out the relation between the quantum SU(2) group and the Askey - Wilson polynomials 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 Al - Salam and Chihara polynomials and the quantised universal enveloping algebra for su( 1, 1 ) is given. Finally, more examples and other approaches as well as some open problems are given.
Palabras claves. Quantum groups, special functions, Hopf algebras, Askey - Wilson polynomials, addition formula, convolution.
