On a local conjecture of Jacquet, ladder representations and standard modules

Maxim Gurevich

doi:10.1007/s00209-015-1522-8

On a local conjecture of Jacquet, ladder representations and standard modules

Maxim Gurevich

Mathematics

Technion - Israel Institute of Technology

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

Abstract

Let E / F be a quadratic extension of p-adic fields. We prove that every smooth irreducible ladder representation of the group GL_n(E) which is contragredient to its own Galois conjugate, possesses the expected distinction properties relative to the subgroup GL_n(F). This affirms a conjecture attributed to Jacquet for a large class of representations. Along the way, we prove a reformulation of the conjecture which concerns standard modules in place of irreducible representations.

Original language	English
Pages (from-to)	1111-1127
Number of pages	17
Journal	Mathematische Zeitschrift
Volume	281
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-015-1522-8
State	Published - 1 Dec 2015

Keywords

Distinguished representations
Ladder representations
Standard modules
p-adic groups

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00209-015-1522-8

Cite this

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abstract = "Let E / F be a quadratic extension of p-adic fields. We prove that every smooth irreducible ladder representation of the group GLn(E) which is contragredient to its own Galois conjugate, possesses the expected distinction properties relative to the subgroup GLn(F). This affirms a conjecture attributed to Jacquet for a large class of representations. Along the way, we prove a reformulation of the conjecture which concerns standard modules in place of irreducible representations.",

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AB - Let E / F be a quadratic extension of p-adic fields. We prove that every smooth irreducible ladder representation of the group GLn(E) which is contragredient to its own Galois conjugate, possesses the expected distinction properties relative to the subgroup GLn(F). This affirms a conjecture attributed to Jacquet for a large class of representations. Along the way, we prove a reformulation of the conjecture which concerns standard modules in place of irreducible representations.

KW - Distinguished representations

KW - Ladder representations

KW - Standard modules

KW - p-adic groups

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DO - 10.1007/s00209-015-1522-8

M3 - مقالة

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EP - 1127

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

On a local conjecture of Jacquet, ladder representations and standard modules

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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