A complex flag manifold is a quotient of a complex semi-simple Lie group by a parabolic subgroup (a subgroup which contains a Borel subgroup). Basic examples are complex projective space and the complex Grassmannians. Now all complex Grassmannian spaces are symmetric spaces, my question is: Which complex flag manifolds are symmetric?

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## **closed** as too localized by José Figueroa-O'Farrill, S. Carnahan♦ Nov 16 '10 at 2:49

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Differential Geometry, Lie Groups, and Symmetric Spacesfor a thorough treatment of both real and complex Lie groups in this setting. (Like most Wikipedia articles, the reference list is unbalanced though the article itself has some useful information.) – Jim Humphreys Nov 15 '10 at 21:51