Duality, central characters, and real-valued characters of finite groups of Lie type

Abstract

We prove that the duality operator preserves the Frobenius--Schur indicators of characters of connected reductive groups of Lie type with connected center. This allows us to extend a result of D. Prasad which relates the Frobenius--Schur indicator of a regular real-valued character to its central character. We apply these results to compute the Frobenius--Schur indicators of certain real-valued, irreducible, Frobenius-invariant Deligne--Lusztig characters, and the Frobenius--Schur indicators of real-valued regular and semisimple characters of finite unitary groups.