
SIGMA 3 (2007), 052, 19 pages math.CA/0702107
https://doi.org/10.3842/SIGMA.2007.052
Polynomials Associated with Dihedral Groups
Charles F. Dunkl
Department of Mathematics, University of Virginia,
Charlottesville, VA 229044137, USA
Received February 06, 2007; Published online March 22, 2007
Abstract
There is a commutative algebra of differentialdifference 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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