Lectures on Dunkl operators

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.

Notes of series of lectures held during the 1997 workshop ``Harmonic analysis on homogeneous spaces and representation of Lie groups'', RIMS, Kyoto, Japan

References in corpus (2)

• A recursion and a combinatorial formula for Jack polynomials
• On q-analogues of Riemann's zeta

Cited by in corpus (9)

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• On the evaluation formula for Jack polynomials with prescribed symmetry
• Inversion formula for the hypergeometric Fourier transform associated with a root system of type $BC$
• Generalised discriminants, deformed quantum Calogero-Moser system and Jack polynomials
• Spherical inversion for a small $K$-type on the split real Lie group of type $G_2$
• Explicit Computations for the Classical and Quantum Integrability of the 3-Dimensional Rational Calogero-Moser System