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Stable base change for spherical functions

Published online by Cambridge University Press:  22 January 2016

Yuval Z. Flicker
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Let E/F be an unramified cyclic extension of local non-archimedean fields, G a connected reductive group over F, K(F) (resp. K(E)) a hyper-special maximal compact subgroup of G(F) (resp. G(E)), and H(F) (resp. H(E)) the Hecke convolution algebra of compactly-supported complex-valued K(F) (resp. G(E))-biinvariant functions on G(F) (resp. G(E)). Then the theory of the Satake transform defines (see § 2) a natural homomorphism H(E) → H(F), θ→f. There is a norm map N from the set of stable twisted conjugacy classes in G(E) to the set of stable conjugacy classes in G(F); it is an injection (see [Ko]). Let Ω‱(x, f) denote the stable orbital integral of f in H(F) at the class x, and Ω‱(y, θ) the stable twisted orbital integral of θ in H(E) at the class y.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 106 , June 1987 , pp. 121 - 142
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

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