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15 September 2009 The base change fundamental lemma for central elements in parahoric Hecke algebras
Thomas J. Haines
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Duke Math. J. 149(3): 569-643 (15 September 2009). DOI: 10.1215/00127094-2009-045


Let G be an unramified group over a p-adic field F, and let E/F be a finite unramified extension field. Let θ denote a generator of Gal(E/F). This article concerns the matching, at all semisimple elements, of orbital integrals on G(F) with θ-twisted orbital integrals on G(E). More precisely, suppose that φ belongs to the center of a parahoric Hecke algebra for G(E). This article introduces a base change homomorphism φbφ taking values in the center of the corresponding parahoric Hecke algebra for G(F). It proves that the functions φ and bφ are associated in the sense that the stable orbital integrals (for semisimple elements) of bφ can be expressed in terms of the stable twisted orbital integrals of φ. In the special case of spherical Hecke algebras (which are commutative), this result becomes precisely the base change fundamental lemma proved previously by Clozel [Cl4] and Labesse [L1]. As has been explained in [H1], the fundamental lemma proved in this article is a key ingredient for the study of Shimura varieties with parahoric level structure at the prime p


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Thomas J. Haines. "The base change fundamental lemma for central elements in parahoric Hecke algebras." Duke Math. J. 149 (3) 569 - 643, 15 September 2009.


Published: 15 September 2009
First available in Project Euclid: 24 August 2009

zbMATH: 1194.22019
MathSciNet: MR2553880
Digital Object Identifier: 10.1215/00127094-2009-045

Primary: 22E50
Secondary: 20G25

Rights: Copyright © 2009 Duke University Press


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Vol.149 • No. 3 • 15 September 2009
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