Closed orbits on partial flag varieties and double flag variety of finite type

Details Closed orbits on partial flag varieties and double flag variety of finite type Closed orbits on partial flag varieties and double flag variety of finite type

2012-04-05

arxiv.org/abs/1204.1118v1

Mathematics

Representation Theory

7 pages

Scientific paper

Let $ G $ be a connected reductive algebraic group over $ \C $. We denote by $ K = (G^{\theta})_{0} $ the identity component of the fixed points of an involutive automorphism $ \theta $ of $ G $. The pair $ (G, K) $ is called a symmetric pair. Let $Q$ be a parabolic subgroup of $K$. We want to find a pair of parabolic subgroups $P_{1}$, $P_{2}$ of $G$ such that (i) $P_{1} \cap P_{2} = Q$ and (ii) $P_{1} P_{2}$ is dense in $G$. The main result of this article states that, for a simple group $G$, we can find such a pair if and only if $(G, K)$ is a Hermitian symmetric pair. The conditions (i) and (ii) yield to conclude that the $K$-orbit through the origin $(e P_{1}, e P_{2})$ of $G/P_{1} \times G/P_{2}$ is closed and it generates an open dense $G$-orbit on the product of partial flag variety. From this point of view, we also give a complete classification of closed $K$-orbits on $G/P_{1} \times G/P_{2}$.

Affiliated with

Also associated with

No associations

Rating

Closed orbits on partial flag varieties and double flag variety of finite type 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 Closed orbits on partial flag varieties and double flag variety of finite type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Closed orbits on partial flag varieties and double flag variety of finite type will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-212232