Geodesic
Vector Polynomials and a Matrix Weight Associated to Dihedral Groups
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SIGMA_2014_10_a43,
     author = {Charles F. Dunkl},
     title = {Vector {Polynomials} and {a~Matrix} {Weight} {Associated} to {Dihedral} {Groups}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a43/}
}
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Charles F. Dunkl. Vector Polynomials and a Matrix Weight Associated to Dihedral Groups. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a43/

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