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Symmetry, Integrability and Geometry: Methods and Applications, 2014, Volume 10, 044, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2014.044
(Mi sigma909)
 

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
Full-text PDF (398 kB) Citations (2)
References:
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
Bibliographic databases:
Document Type: Article
MSC: 33C52; 20F55; 33C45
Language: English
Citation: Charles F. Dunkl, “Vector Polynomials and a Matrix Weight Associated to Dihedral Groups”, SIGMA, 10 (2014), 044, 23 pp.
Citation in format AMSBIB
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\by Charles~F.~Dunkl
\paper Vector Polynomials and a~Matrix Weight Associated to Dihedral Groups
\jour SIGMA
\yr 2014
\vol 10
\papernumber 044
\totalpages 23
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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    Abstract page:140
    Full-text PDF :50
    References:46
     
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