| The sign character for Coxeter groups and the Steinberg character for finite groups with BN-pair can be expressed as alternating sums of permutation characters. We show that we can use the corresponding permutation modules to construct modules which afford these characters.;Further, we consider an analogue of the Steinberg character for GL n Z/ph Z , h ≥ 2, given by Hill. Using the same method as for the sign character and Steinberg character, we construct a module which affords this character. In addition, we show that this character can also be expressed as an alternating sum of permutation characters over certain subgroups of GLn Z/phZ containing B, the subgroup of upper triangular matrices. |
