Duke Mathematical Journal

Uniqueness property for spherical homogeneous spaces

Ivan V. Losev

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Abstract

Let $G$ be a connected reductive group. Recall that a homogeneous $G$-space $X$ is called spherical if a Borel subgroup $B\subset G$ 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

Article information

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

Dates
First available in Project Euclid: 17 March 2009

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1237295911

Digital Object Identifier
doi:10.1215/00127094-2009-013

Mathematical Reviews number (MathSciNet)
MR2495078

Zentralblatt MATH identifier
05544153

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

Citation

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


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