The prasad conjectures for GSp4 and PGSp4

Hengfei Lu; Shou Wu Zhang

doi:10.2140/ant.2020.14.2417

The prasad conjectures for GSp₄ and PGSp₄

Hengfei Lu
, Shou Wu Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We use the theta correspondence between GSp₄(E) and GO(V) to study the GSp₄-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 (GSp₄(E); GSp_1,1(F)), where GSp_1,1 is the unique inner form of GSp₄ defined over F. Then we verify the Prasad conjecture for a discrete series representation τ of PGSp₄(E).

Original language	English (US)
Pages (from-to)	2417-2480
Number of pages	64
Journal	Algebra and Number Theory
Volume	14
Issue number	9
DOIs	https://doi.org/10.2140/ant.2020.14.2417
State	Published - 2020

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Langlands correspondence
Quaternionic hermitian groups
See-saw diagrams
The prasad conjecture
Theta lift

Access to Document

10.2140/ant.2020.14.2417

Cite this

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abstract = "We use the theta correspondence between GSp4(E) and GO(V) to study the GSp4-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 (GSp4(E); GSp1,1(F)), where GSp1,1 is the unique inner form of GSp4 defined over F. Then we verify the Prasad conjecture for a discrete series representation τ of PGSp4(E).",

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AB - We use the theta correspondence between GSp4(E) and GO(V) to study the GSp4-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 (GSp4(E); GSp1,1(F)), where GSp1,1 is the unique inner form of GSp4 defined over F. Then we verify the Prasad conjecture for a discrete series representation τ of PGSp4(E).

KW - Langlands correspondence

KW - Quaternionic hermitian groups

KW - See-saw diagrams

KW - The prasad conjecture

KW - Theta lift

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