On characters of Chevalley groups vanishing at the non-semisimple elements

Abstract

Let [Formula: see text] be a finite simple group of Lie type. In this paper, we study characters of [Formula: see text] that vanish at the non-semisimple elements and whose degree is equal to the order of a maximal unipotent subgroup of [Formula: see text]. Such characters can be viewed as a natural generalization of the Steinberg character. For groups [Formula: see text] of small rank we also determine the characters of this degree vanishing only at the non-identity unipotent elements.