A Description of the Steinberg Character using Gelfand\u2013Graev Characters

Let G be an adjoint finite group of Lie type. In this paper we classify the irreducible characters of G which appear with multiplicity 1 in any Gelfand\u2013Graev character of G. Except for groups of type 2^A_2m and 2^G_2, this property identifies the Steinberg character of G (modulo linear characters)