Local root numbers and spectrum of the local descents for orthogonal groups: P-adic case

Dihua Jiang; Lei Zhang

doi:10.2140/ant.2018.12.1489

Local root numbers and spectrum of the local descents for orthogonal groups: P-adic case

Dihua Jiang, Lei Zhang

Mathematics

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

2 Scopus citations

Abstract

We investigate the local descents for special orthogonal groups over p-adic local fields of characteristic zero, and obtain explicit spectral decomposition of the local descents at the first occurrence index in terms of the local Langlands data via the explicit local Langlands correspondence and explicit calculations of relevant local root numbers. The main result can be regarded as a refinement of the local Gan–Gross– Prasad conjecture (2012).

Original language	English (US)
Pages (from-to)	1489-1535
Number of pages	47
Journal	Algebra and Number Theory
Volume	12
Issue number	6
DOIs	https://doi.org/10.2140/ant.2018.12.1489
State	Published - 2018

Bibliographical note

Funding Information:
The research of Jiang is supported in part by the NSF Grants DMS–1301567 and DMS–1600685, and that of Zhang is supported in part by the National University of Singapore’s start-up grant. MSC2010: primary 11F70; secondary 11S25, 20G25, 22E50. Keywords: restriction and local descent, generic local Arthur packet, local Langlands correspondence, local root numbers, local Gan–Gross–Prasad conjecture.

Publisher Copyright:
© 2018, Mathematical Sciences Publishers. All rights reserved.

Keywords

Generic local Arthur packet
Local Gan-Gross-Prasad conjecture
Local Langlands correspondence
Local root numbers
Restriction and local descent

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title = "Local root numbers and spectrum of the local descents for orthogonal groups: P-adic case",

abstract = "We investigate the local descents for special orthogonal groups over p-adic local fields of characteristic zero, and obtain explicit spectral decomposition of the local descents at the first occurrence index in terms of the local Langlands data via the explicit local Langlands correspondence and explicit calculations of relevant local root numbers. The main result can be regarded as a refinement of the local Gan–Gross– Prasad conjecture (2012).",

keywords = "Generic local Arthur packet, Local Gan-Gross-Prasad conjecture, Local Langlands correspondence, Local root numbers, Restriction and local descent",

author = "Dihua Jiang and Lei Zhang",

note = "Funding Information: The research of Jiang is supported in part by the NSF Grants DMS–1301567 and DMS–1600685, and that of Zhang is supported in part by the National University of Singapore{\textquoteright}s start-up grant. MSC2010: primary 11F70; secondary 11S25, 20G25, 22E50. Keywords: restriction and local descent, generic local Arthur packet, local Langlands correspondence, local root numbers, local Gan–Gross–Prasad conjecture. Publisher Copyright: {\textcopyright} 2018, Mathematical Sciences Publishers. All rights reserved.",

year = "2018",

doi = "10.2140/ant.2018.12.1489",

language = "English (US)",

volume = "12",

pages = "1489--1535",

journal = "Algebra and Number Theory",

issn = "1937-0652",

publisher = "Mathematical Sciences Publishers",

number = "6",

}

TY - JOUR

T1 - Local root numbers and spectrum of the local descents for orthogonal groups

T2 - P-adic case

AU - Jiang, Dihua

AU - Zhang, Lei

N1 - Funding Information: The research of Jiang is supported in part by the NSF Grants DMS–1301567 and DMS–1600685, and that of Zhang is supported in part by the National University of Singapore’s start-up grant. MSC2010: primary 11F70; secondary 11S25, 20G25, 22E50. Keywords: restriction and local descent, generic local Arthur packet, local Langlands correspondence, local root numbers, local Gan–Gross–Prasad conjecture. Publisher Copyright: © 2018, Mathematical Sciences Publishers. All rights reserved.

PY - 2018

Y1 - 2018

N2 - We investigate the local descents for special orthogonal groups over p-adic local fields of characteristic zero, and obtain explicit spectral decomposition of the local descents at the first occurrence index in terms of the local Langlands data via the explicit local Langlands correspondence and explicit calculations of relevant local root numbers. The main result can be regarded as a refinement of the local Gan–Gross– Prasad conjecture (2012).

AB - We investigate the local descents for special orthogonal groups over p-adic local fields of characteristic zero, and obtain explicit spectral decomposition of the local descents at the first occurrence index in terms of the local Langlands data via the explicit local Langlands correspondence and explicit calculations of relevant local root numbers. The main result can be regarded as a refinement of the local Gan–Gross– Prasad conjecture (2012).

KW - Generic local Arthur packet

KW - Local Gan-Gross-Prasad conjecture

KW - Local Langlands correspondence

KW - Local root numbers

KW - Restriction and local descent

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SP - 1489

EP - 1535

JO - Algebra and Number Theory

JF - Algebra and Number Theory

SN - 1937-0652

IS - 6

ER -

Local root numbers and spectrum of the local descents for orthogonal groups: P-adic case

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