Flag Manifold

For any sequence of integers , there is a flag manifold of type (, ..., ) which is the collection of ordered sets of vector subspaces of  (, ..., ) with  and  a subspace of . There are also complex flag manifolds with complex subspaces of  instead of real subspaces of a real -space.

These flag manifolds admit the structure of manifolds in a natural way and are used in the theory of Lie groups.

REFERENCES:

Lu, J.-H. and Weinstein, A. "Poisson Lie Groups, Dressing Transformations, and the Bruhat Decomposition." J. Diff. Geom. 31, 501-526, 1990.