Flag Manifold

For any sequence of integers 0<n_1<...<n_k, there is a flag manifold of type (n_1, ..., n_k) which is the collection of ordered sets of vector subspaces of R^(n_k) (V_1, ..., V_k) with dim(V_i)=n_i and V_i a subspace of V_(i+1). There are also complex flag manifolds with complex subspaces of C^(n_k) instead of real subspaces of a real n_k-space.

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

See also

Grassmann Manifold

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

Referenced on Wolfram|Alpha

Flag Manifold

Cite this as:

Weisstein, Eric W. "Flag Manifold." From MathWorld--A Wolfram Web Resource.

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