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This article is cited in 7 scientific papers (total in 7 papers)
Polynomials Associated with Dihedral Groups
Charles F. Dunkl Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA
Abstract:
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial derivatives. This paper presents an explicit form of the action of the intertwining operator on polynomials by use of harmonic and Jacobi polynomials. The last section of the paper deals with parameter values for which the formulae have singularities.
Keywords:
intertwining operator; Jacobi polynomials.
Received: February 6, 2007; Published online March 22, 2007
Citation:
Charles F. Dunkl, “Polynomials Associated with Dihedral Groups”, SIGMA, 3 (2007), 052, 19 pp.
Linking options:
https://www.mathnet.ru/eng/sigma178 https://www.mathnet.ru/eng/sigma/v3/p52
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Abstract page: | 168 | Full-text PDF : | 47 | References: | 32 |
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