Computation of weight lattices of G-varieties

Details Computation of weight lattices of G-varieties Computation of weight lattices of G-varieties

2007-09-05

arxiv.org/abs/0709.0667v1

J. Math. Sci. 161(2009), 70-96

Mathematics

Algebraic Geometry

29 pages

Scientific paper

Let G be a connected reductive group. To any irreducible G-variety one assigns the lattice generated by 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.

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