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

TL;DR

This paper develops a method to derive orthogonal polynomials associated with compact simple Lie groups, explicitly computing new cases for B_3 and C_3, revealing deep connections to multivariable orthogonal polynomial theory.

Contribution

It introduces a general method for constructing orthogonal polynomials of compact Lie groups and explicitly computes new polynomial cases for B_3 and C_3.

Findings

Derived polynomials for B_3 and C_3 groups

Established connections to multivariable orthogonal polynomials

Provided a systematic approach for rank ≤ 3 Lie groups

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 not greater then 3 are explicitly studied. We derive the polynomials of simple Lie groups B_3 and C_3 as they are not available elsewhere. The results point to far reaching Lie theoretical connections to the theory of multivariable orthogonal polynomials.