English

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.

Keywords

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