Mathematics – Representation Theory
Scientific paper
2011-04-13
Mathematics
Representation Theory
28 pages
Scientific paper
Let $G$ be a connected reductive algebraic group over an algebraically closed field ${\bf k}$ of characteristic not equal to 2, let $\B$ be the variety of all Borel subgroups of $G$, and let $K$ be a symmetric subgroup of $G$. Fixing a closed $K$-orbit in $\B$, we associate to every $K$-orbit on $\B$ some subsets of the Weyl group of $G$, and we study them as invariants of the $K$-orbits. When ${\bf k} = {\mathbb C}$, these invariants are used to determine when an orbit of a real form of $G$ and an orbit of a Borel subgroup of $G$ have non-empty intersection in $\B$. We also characterize the invariants in terms of admissible paths in the set of $K$-orbits in $\B$.
Evens Sam
Lu Jiang-Hua
No associations
LandOfFree
On some invariants of orbits in the flag variety under a symmetric subgroup does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On some invariants of orbits in the flag variety under a symmetric subgroup, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On some invariants of orbits in the flag variety under a symmetric subgroup will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-164862