  In this article we study the representations of general linear groups which
arise from their action on flag spaces. These representations can be decomposed
into irreducibles by proving that the associated Hecke algebra is cellular. We
give a geometric interpretation of a cellular basis of such Hecke algebras
which was introduced by Murphy in the case of finite fields. We apply these
results to decompose representations which arise from the space of modules over
principal ideal local rings of length two with a finite residue field.

Representation Theory