On the spectral decomposition of affine Hecke algebras

Eric M. Opdam (Universiteit van Amsterdam; the Netherlands)

On the spectral decomposition of affine Hecke algebras

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arxiv math/0101007 v4 pith:EJLGMVII submitted 2001-01-01 math.RT

Eric M. Opdam (Universiteit van Amsterdam , the Netherlands) This is my paper · ORCID

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keywords affineheckealgebracertainintegralspecsubalgebraabelian

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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).

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Weights and characters for affine Hecke algebras
math.RT 2026-07 accept novelty 6.5 of 10

Weights uniquely determine simple modules for quasi-simply-connected affine Hecke algebras, and induction/restriction along isogenies preserve semisimplicity, Hermitian duals and unitarity.

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