Sign changes in harmonic analysis on reductive groups

Source abstract

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