Orthogonal polynomials of compact simple Lie groups: branching rules for polynomials

Abstract

Polynomials in this paper are defined starting from a compact semisimple Lie group. A known classification of maximal, semisimple subgroups of simple Lie groups is used to select the cases to be considered here. A general method is presented and all the cases of rank ⩽3 are explicitly studied. We derive the polynomials of simple Lie groups B3 and C3 as they are not available elsewhere. The results point to far reaching Lie theoretical connections to the theory of multivariable orthogonal polynomials.