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).
Bibliographical noteFunding 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.
© 2018, Mathematical Sciences Publishers. All rights reserved.
- Generic local Arthur packet
- Local Gan-Gross-Prasad conjecture
- Local Langlands correspondence
- Local root numbers
- Restriction and local descent