An analogue of the Steinberg character for the general linear group over the integers modulo a prime power

Lees, and independently Hill, described an irreducible character of GLn(Z/phZ) for h>1, which is an analogue of the Steinberg character in the h=1 case. We give a new construction of this analogue. In particular, we prove that it is induced from the Steinberg character of an appropriate parabolic subgroup. Further, we use this to show that it has a characterisation identical to that given by Curtis to the Steinberg character.