Two types of E–discretization of tori of compact semisimple Lie groups

Abstract

We consider a compact semisimple Lie group together with its corresponding affine Weyl group. There are two cases of even affine Weyl subgroups. In the first case, given two positive integers M1, M2, we introduce a finite set of lattice points FeM1,M2; similar lattice set FeM is also constructed in the second case. Each even affine Weyl group then determines the symmetry of its corresponding lattice set as well as one type of E–function. We review the construction of maximal sets of pairwise orthogonal E–functions over the lattice grids. The entire construction of E–functions, discrete lattices and sets, discrete transforms and their application to interpolation is demonstrated for the case of the group SU(3) × SU(3).