Abstract
Let be an unramified group over a -adic field , and let be a finite unramified extension field. Let denote a generator of . This article concerns the matching, at all semisimple elements, of orbital integrals on with -twisted orbital integrals on . More precisely, suppose that belongs to the center of a parahoric Hecke algebra for . This article introduces a base change homomorphism taking values in the center of the corresponding parahoric Hecke algebra for . It proves that the functions and are associated in the sense that the stable orbital integrals (for semisimple elements) of can be expressed in terms of the stable twisted orbital integrals of . 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
Citation
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. https://doi.org/10.1215/00127094-2009-045
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