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On functoriality of Zelevinski involutions

Published online by Cambridge University Press:  15 October 2004

Kaoru Hiraga
Kaoru Hiraga
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japanhiraga@math.kyoto-u.ac.jp
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Abstract

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In this paper, we present a conjecture on a relation between the Zelevinski involutions for reductive groups over a p-adic field and the conjectural A-packets. As evidence for this conjecture, we prove that the Zelevinski involutions, which are regarded as operators on the space of virtual characters, commute with the endoscopic transfers under the assumption of the fundamental lemma for groups and for Lie algebras.

Keywords

Zelevinski involutionfunctorialityendoscopy22E50 (primary)11F7022E35 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 6 , November 2004 , pp. 1625 - 1656
Copyright
Foundation Compositio Mathematica 2004