Jiri Patera (Centre de Recherches Mathématiques, Université de Montréal, Canada)

An overview of special functions derived from the characters of compact simple Lie groups

Abstract:
   Up to 8 complete orthogonal systems of special functions have been defined for certain of the compact simple Lie groups. Only some of them are described in the literature. Their variables are from the real Euclidean space of dimension equal to the rank of the Lie group. For all Lie groups there are at least 3 such systems, two of them being generally well known. Each system can be discretized: Within the systems the functions are pairwise orthogonal when sampled on a known finite fragment of a lattice of any density. Each system can be transformed to a system of orthogonal polynomials. The discretization of the functions is readily carried over to the corresponding polynomials.