Uniqueness property for spherical homogeneous spaces
arXiv:math/0703543
Abstract
Let G be a connected reductive group. Recall that a G-variety X is called spherical if X is normal and a Borel subgroup of G has an open orbit on X. To a spherical homogeneous G-space one assigns certain combinatorial invariants: the weight lattice, the valuation cone and the set of B-stable prime divisors. We prove that two spherical homogeneous spaces with the same combinatorial invariants are equivariantly isomorphic. Further, we show how to recover the group of G-equivariant automorphisms from these invariants.
v1 25 pages, v2 22 pages, some proofs modified, some notation changed, final section removed, v3 minor modifications made v4 final version, to apper in Duke Math J