Programme leaders: G. van Dijk, T.H. Koornwinder
Central research themes are:
(1) analysis on Lie groups, semisimple symmetric spaces and quantum groups
(2) special functions associated with root systems and their interpretation on the above-mentioned structures
(3) analysis, asymptotics, approximation theoretic properties and algorithmic aspects of special functions and orthogonal polynomials in one variable (including the cases of orthogonal rational functions and orthogonality in a Sobolev space)
(4) approximation problems with relation to potential theory
(5) analysis in several complex variables.
This programme unites a number of themes which are mutually connected and have a stimulating influence on each other. Some themes have a quite algebraic setting, while others belong to calssical analysis. Theme (2) dealing with Heckman-Opdam hypergeometric functions and q-analogues like Macdonald polynomials is a highlight of the programme. A new line within theme (1) is the study of canonical representations for Hermitian and para-Hermitian symmetric spaces, and its relation with Berezin quantization.