Vector Polynomials and a Matrix Weight Associated to Dihedral Groups

Symmetry Integrability and Geometry-Methods and Applications

article

Charles F. Dunkl¹ 

[1] Department of Mathematics, University of Virginia

关键词: standard module;    Gaussian weight;   

DOI  :  10.3842/SIGMA.2014.044

来源: National Academy of Science of Ukraine

【 摘 要 】

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 4 F 3 -series.

【 授权许可】

Unknown