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 (12)

• Orthogonal polynomials associated with root systems
• Antisymmetric Orbit Functions
• E-Orbit Functions
• Discrete orthogonal polynomials and difference equations of several variables
• Inversion of the Pieri formula for Macdonald polynomials
• 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
• Discrete Fourier analysis on fundamental domain of $A_d$ lattice and on simplex in $d$-variables
• Branching rules for the Weyl group orbits of the Lie algebra A(n)
• Three dimensional C-, S- and E-transforms
• Recurrence formulas for Macdonald polynomials of type A
• Orbit functions of SU(n) and Chebyshev polynomials

Cited by in corpus (5)

• Orthogonal polynomials of compact simple Lie groups: Branching rules for polynomials
• Branching rules for Weyl group orbits of simple Lie algebras B(n), C(n) and D(n)
• On the families of polynomials forming a part of the Askey--Wilson scheme and their probabilistic applications
• On immanant functions related to Weyl groups of $A_n$
• A graphical categorification of the two-variable Chebyshev polynomials of the second kind