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.
