Orthogonal root numbers of tempered parameters
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
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.
Description
Acknowledgements: I am grateful to Jack Carlisle for discussing the cohomology of classifying spaces, to Peter Dillery for discussing the cohomology of the Weil group, to my advisor, Tasho Kaletha, for discussing the contents of this article and providing detailed feedback on it, to Karol Koziol for pointing me to Flach’s article [34], and to the referees for their helpful comments. This research was supported by the National Science Foundation RTG grant DMS 1840234 and Jessica Fintzen’s Royal Society University Research Fellowship.
Keywords
Journal Title
Conference Name
Journal ISSN
1432-1807
