# Orthogonal Root Numbers of Tempered Parameters

@inproceedings{Schwein2021OrthogonalRN, title={Orthogonal Root Numbers of Tempered Parameters}, author={David Schwein}, year={2021} }

We show that an orthogonal root number of a tempered L-parameter φ 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 φ. The formula resolves a conjecture of Gross and Reeder and computes root numbers of WeilDeligne representations arising in the work of Hiraga, Ichino, and Ikeda on the Plancherel measure.

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