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arXiv · 2107.02360

Orthogonal Root Numbers of Tempered Parameters

David Schwein
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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.

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David Schwein. 2021-07-06. Orthogonal Root Numbers of Tempered Parameters. https://arxiv.org/abs/2107.02360

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