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

Published online by Cambridge University Press:  20 November 2018

Shu-Yen Pan
Shu-Yen Pan*
Affiliation:
Department of Mathematics, National Tsing Hua University and National Center of Theoretical Sciences, Hsinchu 300, Taiwan e-mail: sypan@math.nthu.edu.tw
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Abstract

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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 and 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

22E5011F2720C33local theta correspondencesupercuspidal representationpreservation principleLanglands functoriality
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 1 , 01 February 2017 , pp. 186 - 219
Copyright
Copyright © Canadian Mathematical Society 2017

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