Duke Mathematical Journal

Uniqueness property for spherical homogeneous spaces

Ivan V. Losev

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Let G be a connected reductive group. Recall that a homogeneous G-space X is called spherical if a Borel subgroup BG has an open orbit on X. To X 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 recover the group of G-equivariant automorphisms of X from these invariants

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Duke Math. J., Volume 147, Number 2 (2009), 315-343.

First available in Project Euclid: 17 March 2009

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Zentralblatt MATH identifier

Primary: 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]


Losev, Ivan V. Uniqueness property for spherical homogeneous spaces. Duke Math. J. 147 (2009), no. 2, 315--343. doi:10.1215/00127094-2009-013. https://projecteuclid.org/euclid.dmj/1237295911

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