Computation of weight lattices of G-varieties

TL;DR

This paper develops algorithms to compute the weight lattices of G-varieties, especially focusing on homogeneous spaces and affine homogeneous vector bundles, providing explicit methods for spaces of rank equal to the group's rank.

Contribution

It introduces new algorithms for calculating weight lattices of G-varieties, including explicit procedures for affine homogeneous spaces of maximal rank.

Findings

Algorithms for computing weight lattices of G-varieties.

Explicit computation methods for affine homogeneous spaces of rank equal to G's rank.

Enhanced understanding of the structure of G-varieties through weight lattice analysis.

Abstract

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.