Vol. 12, No. 6, 2018

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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
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).

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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