## 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.