
SIGMA 10 (2014), 044, 23 pages arXiv:1306.6599
https://doi.org/10.3842/SIGMA.2014.044
Vector Polynomials and a Matrix Weight Associated to Dihedral Groups
Charles F. Dunkl
Department of Mathematics, University of Virginia, PO Box 400137, Charlottesville VA 229044137, USA
Received January 22, 2014, in final form April 10, 2014; Published online April 15, 2014
Abstract
The space of polynomials in two real variables with values in a 2dimensional irreducible module of a dihedral
group is studied as a standard module for Dunkl operators.
The oneparameter case is considered (omitting the twoparameter 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.
Key words:
standard module; Gaussian weight.
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