The local structure theorem for real spherical varieties

TY - JOUR

T1 - The local structure theorem for real spherical varieties

AU - Knop, Friedrich

AU - Krötz, Bernhard

AU - Schlichtkrull, Henrik

PY - 2015/11/26

Y1 - 2015/11/26

N2 - Let be an algebraic real reductive group and a real spherical -variety, that is, it admits an open orbit for a minimal parabolic subgroup . We prove a local structure theorem for . In the simplest case where is homogeneous, the theorem provides an isomorphism of the open -orbit with a bundle . Here is a parabolic subgroup with Levi decomposition , and is a homogeneous space for a quotient of , where is normal, such that is compact modulo center.

AB - Let be an algebraic real reductive group and a real spherical -variety, that is, it admits an open orbit for a minimal parabolic subgroup . We prove a local structure theorem for . In the simplest case where is homogeneous, the theorem provides an isomorphism of the open -orbit with a bundle . Here is a parabolic subgroup with Levi decomposition , and is a homogeneous space for a quotient of , where is normal, such that is compact modulo center.

U2 - 10.1112/s0010437x15007307

DO - 10.1112/s0010437x15007307

M3 - Journal article

SN - 0010-437X

VL - 151

SP - 2145

EP - 2159

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 11

ER -