Lectures on Dunkl operators
Representation Theory
2007-05-23 v1 Spectral Theory
Abstract
These are the lecture notes of a series of lectures on Dunkl operators. We discuss the underlying algebraic structure of the degenerate double affine Hecke algebra, intertwiners and shift operators. We apply this to Macdonald theory. We also discuss the ``compact'' and ``noncompact'' spectral decomposition of these operators. In the attractive noncompact situation we classify the discrete eigenfunctions and compute their square norms.
Cite
@article{arxiv.math/9812007,
title = {Lectures on Dunkl operators},
author = {Eric M. Opdam},
journal= {arXiv preprint arXiv:math/9812007},
year = {2007}
}
Comments
Notes of series of lectures held during the 1997 workshop ``Harmonic analysis on homogeneous spaces and representation of Lie groups'', RIMS, Kyoto, Japan