Computation of weight lattices of G-varieties

Let G be a connected reductive group. To any irreducible G-variety, one assigns the lattice consisting of all weights of B-semiinvariant rational functions on X, where B is a Borel subgroup of G. This lattice is called the weight lattice of X. We establish algorithms for computing weight lattices for homogeneous spaces and affine homogeneous vector bundles. For affine homogeneous spaces of rank rk G we present a more or less explicit computation. © 2009 Springer Science+Business Media, Inc.