Let G be a finite simple group of Lie type. In this paper, we study characters of G that vanish at the non-semisimple elements and whose degree is equal to the order of a maximal unipotent subgroup of G. Such characters can be viewed as a natural generalization of the Steinberg character. For groups G of small rank we also determine the characters of this degree vanishing only at the non-identity unipotent elements.
- Chevalley groups
- Gelfand-Graev characters
- generalized Steinberg characters
- p-singular elements
- projective modules