Geometry of B×B -orbit closures in equivariant embeddings
Abstract
Let
X
denote an equivariant embedding of a connected reductive group
G
over an algebraically closed field
k
. Let
B
denote a Borel subgroup of
G
and let
Z
denote a
B×B
-orbit closure in
X
. When the characteristic of
k
is positive and
X
is projective we prove that
Z
is globally
F
-regular. As a consequence,
Z
is normal and Cohen-Macaulay for arbitrary
X
and arbitrary characteristics. Moreover, in characteristic zero it follows that
Z
has rational singularities. This extends earlier results by the second author and M. Brion.