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Vector Polynomials and a Matrix Weight Associated to Dihedral Groups
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Vector Polynomials and a Matrix Weight Associated to Dihedral Groups
Інший ID:
2010 Mathematics Subject Classification: 33C52; 20F55; 33C45
DOI:10.3842/SIGMA.2014.044
DOI:10.3842/SIGMA.2014.044
Посилання:
Vector Polynomials and a Matrix Weight Associated to Dihedral Groups / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 5 назв. — англ.
Дата:
2014
Переглядів:
480
Завантажень:
238
Анотація:
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 ₄F₃-series.
