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This article is cited in 2 scientific papers (total 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.
Received: January 22, 2014; in final form April 10, 2014; Published online April 15, 2014
Citation:
Charles F. Dunkl, “Vector Polynomials and a Matrix Weight Associated to Dihedral Groups”, SIGMA, 10 (2014), 044, 23 pp.
Linking options:
https://www.mathnet.ru/eng/sigma909 https://www.mathnet.ru/eng/sigma/v10/p44
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Abstract page: | 140 | Full-text PDF : | 50 | References: | 46 |
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