Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 052, 19 pages      math.CA/0702107

Polynomials Associated with Dihedral Groups

Charles F. Dunkl
Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA

Received February 06, 2007; Published online March 22, 2007

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.

Key words: intertwining operator; Jacobi polynomials.

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