#### 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).

##### 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