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# $L$-Functoriality for Local Theta Correspondence of Supercuspidal Representations with Unipotent Reduction

Published:2016-12-06
Printed: Feb 2017
• Shu-Yen Pan,
Department of Mathematics, National Tsing Hua University and National Center of Theoretical Sciences, Hsinchu 300, Taiwan
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## Abstract

The preservation principle of local theta correspondences of reductive dual pairs over a $p$-adic field predicts the existence of a sequence of irreducible supercuspidal representations of classical groups. Adams/Harris-Kudla-Sweet have a conjecture about the Langlands parameters for the sequence of supercuspidal representations. In this paper we prove modified versions of their conjectures for the case of supercuspidal representations with unipotent reduction.
 Keywords: local theta correspondence, supercuspidal representation, preservation principle, Langlands functoriality
 MSC Classifications: 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05] 11F27 - Theta series; Weil representation; theta correspondences 20C33 - Representations of finite groups of Lie type

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