- On the spectral decomposition of affine Hecke algebras
- Document type
- Working paper
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
An affine Hecke algebra H contains a large abelian subalgebra A spanned by the Bernstein-Zelevinski-Lusztig basic elements theta x, where x runs over (an extension of) the root lattice. The center Z of H is the subalgebra of Weyl group invariant elements in A. The 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 shall derivethe Plancherel formula of the affine Hecke algebra by localization of this integral on a certain subset of spec(Z).
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