This article is cited in 2 papers

Vector Polynomials and a Matrix Weight Associated to Dihedral Groups

Charles F. Dunkl

Department of Mathematics, University of Virginia, PO Box 400137, Charlottesville VA 22904-4137, USA

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.

Keywords: standard module; Gaussian weight.

MSC: 33C52; 20F55; 33C45

Received: January 22, 2014; in final form April 10, 2014; Published online April 15, 2014

Language: English

DOI: 10.3842/SIGMA.2014.044

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ArXiv: 1306.6599