Polynomials Associated with Dihedral Groups
Classical Analysis and ODEs
2008-04-24 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.math/0702107,
title = {Polynomials Associated with Dihedral Groups},
author = {Charles F. Dunkl},
journal= {arXiv preprint arXiv:math/0702107},
year = {2008}
}
Comments
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/