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Uniqueness property for spherical homogeneous spaces

Ivan V. Losev
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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.

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Ivan V. Losev. 2008-11-02. Uniqueness property for spherical homogeneous spaces. https://arxiv.org/abs/math/0703543

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