Lenka Hakova (Université de Montréal, Canada)

Generalized E-orbit functions

Abstract:
   Recent discovery of orbit functions of the Weyl group modified by the group of two elements led to the known special functions C and S and also to the new special functions which we denote S^s and S^l. The multivariate E-functions as known for C and S orbit functions turned out to an analog involving the new orbit functions S^s and S^l. We will bring side by side E-functions of old and new types and present their properties, namely their (anti)invariance with respect to certain Weyl subgroups and their orthogonalities on a finite region of an n-dimensional Euclidian space.