Polynomials Associated with Dihedral Groups

Details Polynomials Associated with Dihedral Groups Polynomials Associated with Dihedral Groups

2007-02-05

arxiv.org/abs/math/0702107v2

SIGMA 3 (2007), 052, 19 pages

Mathematics

Classical Analysis and ODEs

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2007.052

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.

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