Positivity of Dunkl's intertwining operator via the trigonometric setting
Abstract
In this note, a new proof for the positivity of Dunkl's intertwining operator in the crystallographic case is given. It is based on an asymptotic relationship between the Opdam-Cherednik kernel and the Dunkl kernel as recently observed by M. de Jeu, and on positivity results of S. Sahi for the Heckman-Opdam polynomials and their non-symmetric counterparts.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- May 2004
- DOI:
- arXiv:
- arXiv:math/0405368
- Bibcode:
- 2004math......5368R
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- Mathematics - Representation Theory;
- 33C52;
- 33C67
- E-Print:
- 9 pages