On local descent for unitary groups

David Soudry; Yaacov Tanay

doi:10.1016/j.jnt.2014.03.003

On local descent for unitary groups

David Soudry^*, Yaacov Tanay

^*Corresponding author for this work

School of Mathematical Sciences

Tel Aviv University

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

13 Scopus citations

Abstract

We study the local descent from irreducible, supercuspidal, self-conjugate representations of GL_2n(E) to irreducible, supercuspidal and generic representations of the quasi-split unitary group U_2n(F) in 2n variables, corresponding to a quadratic extension E/F of p-adic fields. We construct the descent and prove that it is nontrivial, supercuspidal, generic and irreducible. We write the relations with poles of local gamma factors and functoriality. We also consider representations as above of GL_2n+1(E).

Original language	English
Pages (from-to)	557-626
Number of pages	70
Journal	Journal of Number Theory
Volume	146
Issue number	C
DOIs	https://doi.org/10.1016/j.jnt.2014.03.003
State	Published - 2015

Keywords

Functorial lift
Gamma factors
Local descent
Primary
Secondary
Supercuspidal representations
Unitary groups

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10.1016/j.jnt.2014.03.003

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abstract = "We study the local descent from irreducible, supercuspidal, self-conjugate representations of GL2n(E) to irreducible, supercuspidal and generic representations of the quasi-split unitary group U2n(F) in 2n variables, corresponding to a quadratic extension E/F of p-adic fields. We construct the descent and prove that it is nontrivial, supercuspidal, generic and irreducible. We write the relations with poles of local gamma factors and functoriality. We also consider representations as above of GL2n+1(E).",

keywords = "Functorial lift, Gamma factors, Local descent, Primary, Secondary, Supercuspidal representations, Unitary groups",

author = "David Soudry and Yaacov Tanay",

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AU - Soudry, David

AU - Tanay, Yaacov

PY - 2015

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N2 - We study the local descent from irreducible, supercuspidal, self-conjugate representations of GL2n(E) to irreducible, supercuspidal and generic representations of the quasi-split unitary group U2n(F) in 2n variables, corresponding to a quadratic extension E/F of p-adic fields. We construct the descent and prove that it is nontrivial, supercuspidal, generic and irreducible. We write the relations with poles of local gamma factors and functoriality. We also consider representations as above of GL2n+1(E).

AB - We study the local descent from irreducible, supercuspidal, self-conjugate representations of GL2n(E) to irreducible, supercuspidal and generic representations of the quasi-split unitary group U2n(F) in 2n variables, corresponding to a quadratic extension E/F of p-adic fields. We construct the descent and prove that it is nontrivial, supercuspidal, generic and irreducible. We write the relations with poles of local gamma factors and functoriality. We also consider representations as above of GL2n+1(E).

KW - Functorial lift

KW - Gamma factors

KW - Local descent

KW - Primary

KW - Secondary

KW - Supercuspidal representations

KW - Unitary groups

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VL - 146

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EP - 626

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - C

ER -

On local descent for unitary groups

Abstract

Keywords

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