The Prasad conjectures for GSp4 and PGSp4

Lu, Hengfei

doi:10.2140/ant.2020.14.2417

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The Prasad conjectures for $\mathrm{GSp}_4$ and $\mathrm{PGSp}_4$

Hengfei Lu

Vol. 14 (2020), No. 9, 2417–2480

DOI: 10.2140/ant.2020.14.2417

Abstract

We use the theta correspondence between ${GSp}_{4} (E)$ and $GO (V)$ to study the ${GSp}_{4}$ -distinction problems over a quadratic extension $E ∕ F$ of nonarchimedean local fields of characteristic $0$ . With a similar strategy, we investigate the distinction problem for the pair $({GSp}_{4} (E), {GSp}_{1, 1} (F))$ , where ${GSp}_{1, 1}$ is the unique inner form of ${GSp}_{4}$ defined over $F$ . Then we verify the Prasad conjecture for a discrete series representation $\bar{τ}$ of ${PGSp}_{4} (E)$ .

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Keywords

Langlands correspondence, see-saw diagrams, theta lift, quaternionic Hermitian groups, the Prasad conjecture

Mathematical Subject Classification 2010

Primary: 22E50

Secondary: 11F27

Milestones

Received: 7 May 2019

Revised: 8 February 2020

Accepted: 4 May 2020

Published: 13 October 2020

Authors

Hengfei Lu
Department of Mathematics Weizmann Institute of Science Rehovot Israel	Department of Mathematics University of Vienna Vienna Austria

Vol. 14, No. 9, 2020