On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

Natural Sciences and Engineering Research Council of Canada

Natural Sciences and Engineering Research Council of Canada

MIND Research Institute, Santa Ana, California

MIND Research Institute, Santa Ana, California

Ministry of Education of Czech Republic[MSM6840770039]

Ministry of Education of Czech Republic

Centre de recherches mathematiques, Universite de Montreal

Centre de recherches mathematiques, Universite de Montreal