Vector Polynomials and a Matrix Weight Associated to Dihedral Groups
Classical Analysis and ODEs
2014-04-16 v3
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 -series.
Cite
@article{arxiv.1306.6599,
title = {Vector Polynomials and a Matrix Weight Associated to Dihedral Groups},
author = {Charles F. Dunkl},
journal= {arXiv preprint arXiv:1306.6599},
year = {2014}
}