On discretization of tori of compact simple Lie groups: II

Abstract

The discrete orthogonality of special function families, called C- and S-functions, which are derived from the characters of compact simple Lie groups, is described in Hrivnák and Patera (2009 J. Phys. A: Math. Theor. 42 385208). Here, the results of Hrivnák and Patera are extended to two additional recently discovered families of special functions, called Ss- and Sl-functions. The main result is an explicit description of their pairwise discrete orthogonality within each family, when the functions are sampled on finite fragments FsM and FlM of a lattice in any dimension n ⩾ 2 and of any density controlled by M, and of the symmetry of the weight lattice of any compact simple Lie group with two different lengths of roots.