NWO-financed PhD-project
The research group is composed of
Short description: The purpose of this proposal is to investigate the relationship between the representation theory of dynamical quantum groups and the theory of special functions. Dynamical quantum groups are related to solutions of the dynamical Yang-Baxter equation and we focus our attention to the so-called trigonometric and elliptic solutions. We will study representations and co-representations and we intend to establish a fruitful link with classes of special functions, leading to new insights on both sides. In the trigonometric case we expect special functions of basic hypergeometric type, and in the elliptic case we expect special functions of elliptic hypergeometric type. This last class is relatively new, and we intend to study its properties from an analytic point of view. We also intend to investigate the relations to statistical mechanics and Knizhnik-Zamolodchikov equations.