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arXiv · 1306.6599

Vector Polynomials and a Matrix Weight Associated to Dihedral Groups

Charles F. Dunkl
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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 $_4F_3$-series.

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Charles F. Dunkl. 2013-06-27. Vector Polynomials and a Matrix Weight Associated to Dihedral Groups. https://doi.org/10.3842/sigma.2014.044

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