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Date: 11-7-2021
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Date: 24-5-2021
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Date: 13-5-2021
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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.
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