Flag manifold

In mathematics, a flag manifold (or flag variety) is the set of all flags in a finite-dimensional vector space V. The flag variety on V is naturally a projective variety. If the base field K is the real or complex numbers then the flag variety has a natural manifold structure turning it into a smooth or complex manifold.

Related Topics:
Mathematics - Flags - Vector space - Projective variety - Field - Manifold - Smooth - Complex manifold

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Flag manifolds are called complete or partial according to whether one considers complete or partial flags. For partial flags, one needs to specify the sequence of dimensions of the flags under consideration.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~