Abstract
We prove the local Langlands conjecture for $\mathrm{GSp}_4(F)$ where $F$ is a non-archimedean local field of characteristic zero.
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author = {Gan, Wee Teck and Takeda, Shuichiro},
TITLE = {On the regularized {S}iegel-{W}eil formula (the second term identity) and non-vanishing of theta lifts from orthogonal groups},
NOTE={to appear in {\it {J.} {R}eine {A}ngew. {M}ath.}},
DOI = {10.1515/CRELLE.2011.076},
} -
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NOTE={to appear in {\it Represent. Theory}},
ARXIV={1006.3367},
} -
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MRNUMBER = {1070599},
MRREVIEWER = {Stephen Gelbart},
DOI = {10.2307/1971524},
} -
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@book {Si, MRKEY = {0544991},
AUTHOR = {Silberger, Allan J.},
TITLE = {Introduction to Harmonic Analysis on Reductive {$p$}-adic Groups},
SERIES = {Math. Notes},
VOLUME = {23},
PUBLISHER = {Princeton Univ. Press},
ADDRESS = {Princeton, N.J.},
YEAR = {1979},
PAGES = {iv+371},
ISBN = {0-691-08246-4},
MRCLASS = {22E50 (43A65 43A80)},
MRNUMBER = {0544991},
MRREVIEWER = {J. Szmidt},
ZBLNUMBER = {0458.22006},
} -
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@article {So, MRKEY = {0917359},
AUTHOR = {Soudry, David},
TITLE = {A uniqueness theorem for representations of {${\rm GSO}(6)$} and the strong multiplicity one theorem for generic representations of {${\rm GSp}(4)$}},
JOURNAL = {Israel J. Math.},
FJOURNAL = {Israel Journal of Mathematics},
VOLUME = {58},
YEAR = {1987},
NUMBER = {3},
PAGES = {257--287},
ISSN = {0021-2172},
CODEN = {ISJMAP},
MRCLASS = {22E55 (22E50)},
MRNUMBER = {0917359},
MRREVIEWER = {Marko Tadi{ć}},
DOI = {10.1007/BF02771692},
ZBLNUMBER = {0642.22003},
} -
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@article {ST, MRKEY = {1212952},
AUTHOR = {Sally, Jr., Paul J. and Tadi{ć},
Marko},
TITLE = {Induced representations and classifications for {${\rm GSp}(2,F)$} and {${\rm Sp}(2,F)$}},
JOURNAL = {Mém. Soc. Math. France},
FJOURNAL = {Mémoires de la Société Mathématique de France. Nouvelle Série},
NUMBER = {52},
YEAR = {1993},
PAGES = {75--133},
ISSN = {0037-9484},
MRCLASS = {22E50},
MRNUMBER = {1212952},
MRREVIEWER = {Leticia Barchini},
ZBLNUMBER = {0784.22008},
} -
[V] M. Vignéras, "Correspondances entre representations automorphes de ${ GL}(2)$ sur une extension quadratique de ${ GSp}(4)$ sur ${\bf Q}$, conjecture locale de Langlands pour ${ GSp}(4)$," in The Selberg Trace Formula and Related Topics, Providence, RI, 1986, pp. 463-527.
@inproceedings {V, MRKEY = {0853573},
AUTHOR = {Vign{é}ras, Marie-France},
TITLE = {Correspondances entre representations automorphes de {${\rm GL}(2)$} sur une extension quadratique de {${\rm GSp}(4)$} sur {${\bf Q}$},
conjecture locale de {L}anglands pour {${\rm GSp}(4)$}},
BOOKTITLE = {The {S}elberg Trace Formula and Related Topics},
VENUE={{B}runswick, {M}aine, 1984},
SERIES = {Contemp. Math.},
VOLUME = {53},
PAGES = {463--527},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1986},
MRCLASS = {11S37 (11F70 22E50 22E55)},
MRNUMBER = {0853573},
MRREVIEWER = {J. G. M. Mars},
ZBLNUMBER = {0595.12009},
} -
[Z] W. Zink, Letter to M.-F. Vigneras (1984).
@misc{Z,
author={Zink, W.},
TITLE={letter to {M.-F. V}igneras (1984)},
}