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 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.

28 pages, 7 figures, 8 tables

References in corpus (5)

• Antisymmetric Orbit Functions
• E-Orbit Functions
• Orthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group
• Orthogonal polynomials of compact simple Lie groups: Branching rules for polynomials
• Three dimensional C-, S- and E-transforms

Cited by in corpus (1)

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