The local structure theorem for real spherical varieties

Friedrich Knop; Bernhard Krötz; Henrik Schlichtkrull

doi:10.1112/s0010437x15007307

The local structure theorem for real spherical varieties

Friedrich Knop, Bernhard Krötz, Henrik Schlichtkrull

Institut for Matematiske Fag

10 Citationer (Scopus)

Abstract

Let G be an algebraic real reductive group and Z a real spherical G -variety, that is, it admits an open orbit for a minimal parabolic subgroup P . We prove a local structure theorem for Z . In the simplest case where Z is homogeneous, the theorem provides an isomorphism of the open P -orbit with a bundle Q×LS . Here Q is a parabolic subgroup with Levi decomposition L⋉U , and S is a homogeneous space for a quotient D=L/Ln of L , where Ln⊆L is normal, such that D is compact modulo center.

Originalsprog	Engelsk
Tidsskrift	Compositio Mathematica
Vol/bind	151
Udgave nummer	11
Sider (fra-til)	2145-2159
Antal sider	15
ISSN	0010-437X
DOI	https://doi.org/10.1112/s0010437x15007307
Status	Udgivet - 26 nov. 2015

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10.1112/s0010437x15007307

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The local structure theorem for real spherical varieties

Abstract

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