The local structure theorem for real spherical varieties
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
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Journal | Compositio Mathematica |
Volume | 151 |
Issue number | 11 |
Pages (from-to) | 2145-2159 |
Number of pages | 15 |
ISSN | 0010-437X |
DOIs | |
Publication status | Published - 2015 |
ID: 149086369