Polynomials Associated with Dihedral Groups
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.
- Publication:
-
SIGMA
- Pub Date:
- March 2007
- DOI:
- 10.3842/SIGMA.2007.052
- arXiv:
- arXiv:math/0702107
- Bibcode:
- 2007SIGMA...3..052D
- Keywords:
-
- intertwining operator;
- Jacobi polynomials;
- Mathematics - Classical Analysis and ODEs;
- Mathematical Physics;
- Primary 33C45;
- 33C80;
- Secondary 20F55
- E-Print:
- Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/