Antisymmetric exponential functions and (anti)symmetric multivariate Fourier and trigonometric transforms

Abstract:
The talk represents the results on multivariate symmetric and antisymmetric functions and transforms, obtained together with Prof. J. Patera. Multivariate exponential functions, antisymmetric with respect to a Weyl group W of a simple Lie algebra, are studied. They are eigenfunctions of the Laplace operator vanishing on the boundary of the fundamental domain of the affine Weyl group, corresponding to the Weyl group W. Multivariate symmetric and antisymmetric continuous and finite Fourier transforms are constructed. Multivariate symmetric and antisymmetric sine and cosine functions are given. By means of these functions, multivariate symmetric and antisymmetric continuous and finite sine and cosine transforms are obtained.

Joint work with Jiri Patera (Centre de Recherches Mathématiques, Université de Montréal, Canada).