Talk Abstracts FRG Workshop and Conference on Characters, Liftings, and Types

Jeffrey Adams, University of Maryland. The Chevalley Involution for Real Groups, with applications to the Fubini-Schur Indicator. The Chevalley involution of a complex group is unique up to conjugation, and takes any algebraic representation to its contragredient. The analogue over local fields is subtle. We prove that the Chevalley involution is defined over R, and with an appropriate condition is unique up to conjuguation by G(R). We deduce some results on groups for which every irreducible representation is self-dual, and the Fubini-Schur (symplectic/orthogonal) indicator of self-dual representations.