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

Jiang, Dihua; Zhang, Lei

doi:10.2140/ant.2018.12.1489

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

Dihua Jiang and Lei Zhang

Vol. 12 (2018), No. 6, 1489–1535

DOI: 10.2140/ant.2018.12.1489

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

restriction and local descent, generic local Arthur packet, local Langlands correspondence, local root numbers, local Gan–Gross–Prasad conjecture

Mathematical Subject Classification 2010

Primary: 11F70

Secondary: 11S25, 20G25, 22E50

Milestones

Received: 1 October 2017

Revised: 29 December 2017

Accepted: 15 April 2018

Published: 6 October 2018

Authors

Dihua Jiang
School of Mathematics University of Minnesota Minneapolis, MN United States

Lei Zhang
Department of Mathematics National University of Singapore Singapore

Vol. 12, No. 6, 2018