On the spectral decomposition of affine Hecke algebras
Representation Theory
2007-05-23 v4
Abstract
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 algebra can be written as an integral of a rational form (with values in the linear dual of H) over a certain cycle in the algebraic torus T=spec(A). We derive the Plancherel formula of the affine Hecke algebra by localization of this integral on a certain subset of spec(Z).
Keywords
Cite
@article{arxiv.math/0101007,
title = {On the spectral decomposition of affine Hecke algebras},
author = {Eric M. Opdam},
journal= {arXiv preprint arXiv:math/0101007},
year = {2007}
}
Comments
137 pages. Improved notations, the introduction, applications and examples. Corrected a constant factor in Plancherel density product formula, and described the Fourier transform more appropriately. Above all, added an index of notations