English

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!

R2 v1 2026-06-24T03:55:03.237Z