Orthogonal Root Numbers of Tempered Parameters
Number Theory
2021-07-07 v1 Representation Theory
Abstract
We show that an orthogonal root number of a tempered L-parameter decomposes as the product of two other numbers: the orthogonal root number of the principal parameter and the value on a certain involution of Langlands's central character for the parameter. The formula resolves a conjecture of Gross and Reeder and computes root numbers of Weil-Deligne representations arising in the work of Hiraga, Ichino, and Ikeda on the Plancherel measure.
Keywords
Cite
@article{arxiv.2107.02360,
title = {Orthogonal Root Numbers of Tempered Parameters},
author = {David Schwein},
journal= {arXiv preprint arXiv:2107.02360},
year = {2021}
}
Comments
31 pages. Comments welcome!