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Sign changes in harmonic analysis on reductive groups. (English) Zbl 0538.22010
From the author’s 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.” For F local, the sign e(G) coincides with one familiar from character identities. The author suggests also a use in stabilizing orbital integrals for (singular) semisimple elements: This is taken up in his recent paper ”Stable trace formula: elliptic singular terms” (preprint); here the product formula for global e(G) plays a role.
Reviewer: D.Shelstad

MSC:
22E50 Representations of Lie and linear algebraic groups over local fields
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
58J40 Pseudodifferential and Fourier integral operators on manifolds
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