Abstract
We show that an orthogonal root number of a tempered L-parameter varphi decomposes as the product of two other numbers: the orthogonal root number of the principal parameter and the value on a central involution of Langlands’s central character for varphi . The formula resolves a conjecture of Gross and Reeder and computes root numbers of Weil–Deligne representations arising in a conjectural description of the Plancherel measure.
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