Sign changes in harmonic analysis on reductive groups

Kottwitz, Robert E.

doi:10.1090/S0002-9947-1983-0697075-6

Sign changes in harmonic analysis on reductive groups
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by Robert E. Kottwitz

Trans. Amer. Math. Soc. 278 (1983), 289-297

DOI: https://doi.org/10.1090/S0002-9947-1983-0697075-6

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Abstract:

Let $G$ be a connected reductive group over a field $F$. In this note the author constructs an element $e(G)$ of the Brauer group of $F$. The square of this element is trivial. For a local field, $e(G)$ may be regarded as an element of $\{ \pm 1\}$ and is needed for harmonic analysis on reductive groups over that field. For a global field there is a product formula.

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