On the spectral decomposition of affine Hecke algebras

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 $n$ 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).

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