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7 papers
The Schwartz algebra of an affine Hecke algebra
Patrick Delorme, Eric Opdam
For a general affine Hecke algebra H we study its Schwartz completion S. The main theorem is an exact description of the image of S under the Fourier isomorphism. An important ingr…
Dunkl operators for complex reflection groups
C. F. Dunkl, E. M. Opdam
Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parametrized family of deformations of the polynomial De Rham comp…
On the spectral decomposition of affine Hecke algebras
Eric M. Opdam
An affine Hecke algebra H contains a large abelian subalgebra A. The center Z of H is the subalgebra of Weyl group invariant elements in A. The natural trace of the affine Hecke al…
A generating function for the trace of the Iwahori-Hecke algebra
Eric M. Opdam
The Iwahori-Hecke algebra has a ``natural'' trace . This trace is the evaluation at the identity element in the usual interpretation of the Iwahori-Hecke algebra as a sub-algebr…
Lectures on Dunkl operators
Eric M. Opdam
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 an…
Cuspidal hypergeometric functions
Eric M. Opdam
We prove the Plancherel formula for hypergeometric functions associated to a root system in the situation when the root multiplicities are negative (but close to 0). As a result we…