Generalised Kostka-Foulkes polynomials and cohomology of line bundles on homogeneous vector bundles

Abstract

Let $G$ be a semisimple algebraic group and $B$ a Borel subgroup. We consider generalisations of Lusztig's q-analogues of weight multiplicity, where the set of positive roots is replaced with the multiset of weights of a $B$-submodule of an arbitrary finite-dimensional $G$-module.