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ON $\text{Sp}$-DISTINGUISHED REPRESENTATIONS OF THE QUASI-SPLIT UNITARY GROUPS

Part of: Lie groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  17 April 2019

A. Mitra  and
Omer Offen
A. Mitra
Affiliation:
Indian Institute of Science Education and Research, Tirupati, India ([email protected])
Omer Offen
Affiliation:
Brandeis University, Waltham, MA, USA ([email protected])
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Abstract

We study $\text{Sp}_{2n}(F)$-distinction for representations of the quasi-split unitary group $U_{2n}(E/F)$ in $2n$ variables with respect to a quadratic extension $E/F$ of $p$-adic fields. A conjecture of Dijols and Prasad predicts that no tempered representation is distinguished. We verify this for a large family of representations in terms of the Mœglin–Tadić classification of the discrete series. We further study distinction for some families of non-tempered representations. In particular, we exhibit $L$-packets with no distinguished members that transfer under base change to $\text{Sp}_{2n}(E)$-distinguished representations of $\text{GL}_{2n}(E)$.

Keywords

representations of p-adic reductive groupsdistinguished representationsquadratic base change

MSC classification

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 1 , January 2021 , pp. 225 - 276
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Copyright
© Cambridge University Press 2019

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