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On the local theta correspondence and R-groups

Published online by Cambridge University Press:  04 December 2007

Atsushi Ichino
Atsushi Ichino
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japanichino@sci.osaka-cu.ac.jp
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Abstract

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For the reductive dual pair (U(n, n), U(n, n)) over a p-adic field, we study the local theta correspondence for certain tempered representations in terms of R-groups. In the case we consider, the Langlands parameter is preserved, but, a twist occurs in the L-packet. Moreover this twist is determined by root numbers.

Keywords

local theta correspondenceR-groupsroot numbers11F2722E50
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 2 , March 2004 , pp. 301 - 316
Copyright
Foundation Compositio Mathematica 2004