@article{7a7f8996db824397a90a5e4bd47cb7fc,
title = "The prasad conjectures for GSp4 and PGSp4 ",
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).",
keywords = "Langlands correspondence, Quaternionic hermitian groups, See-saw diagrams, The prasad conjecture, Theta lift",
author = "Hengfei Lu and Zhang, {Shou Wu}",
note = "Funding Information: This paper contains part of the author{\textquoteright}s Ph.D. thesis [Lu 2017a]. He is grateful to Wee Teck Gan for the guidance and numerous discussions when he was studying in Singapore. He would like to thank Dipendra Prasad for proposing this conjecture and fruitful discussions. He wants to thank Dmitry Gourevitch and Lei Zhang for useful comments as well. He is also grateful to the anonymous referee for a careful reading of the manuscript and numerous suggestions which greatly improved the exposition of this paper. This work was partially supported by the ERC, StG grant number 637912. Publisher Copyright: {\textcopyright} 2020 Mathematical Sciences Publishers.",
year = "2020",
doi = "10.2140/ant.2020.14.2417",
language = "English (US)",
volume = "14",
pages = "2417--2480",
journal = "Algebra and Number Theory",
issn = "1937-0652",
publisher = "Mathematical Sciences Publishers",
number = "9",
}