Vector Polynomials and a Matrix Weight Associated to Dihedral Groups

Abstract

The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case for even dihedral groups). The matrix weight function for the Gaussian form is found explicitly by solving a boundary value problem, and then computing the normalizing constant. An orthogonal basis for the homogeneous harmonic polynomials is constructed. The coefficients of these polynomials are found to be balanced terminating ${}_4{F}_3$-series.

References in corpus (2)

• Unitary representations of rational Cherednik algebras
• Vector-Valued Polynomials and a Matrix Weight Function with $B_2$-Action

Cited by in corpus (1)

• Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials