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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 052, 19 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.052 (Mi sigma178) 		 
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
Full-text PDF (285 kB) Citations (7)
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DOI: https://doi.org/10.3842/SIGMA.2007.052
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
Bibliographic databases:
Document Type: Article
MSC: 33C45; 33C80; 20F55
Language: English
Citation: Charles F. Dunkl, “Polynomials Associated with Dihedral Groups”, SIGMA, 3 (2007), 052, 19 pp.
Citation in format AMSBIB
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\by Charles F.~Dunkl
\paper Polynomials Associated with Dihedral Groups
\jour SIGMA
\yr 2007
\vol 3
\papernumber 052
\totalpages 19
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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