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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

-1 votes

Is $M=E_{7(7)}/SU(7)\times\mathbb{R}^{+}$ a (pseudo)Kähler-Hodge manifold? Open problem

If i am not wrong the following is true, G compact connected Lie group, H the centralizer of a torus in G, then G/H is a projective manifold, does this answer your question??
jorge vargas's user avatar
1 vote
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Borel–Weil–Bott for partial flag varieties

There are many places that give a complete answer to your question: One is a paper in the Annals of Math written by Kostant around the middle fifties, other more geometrical is due to Griffits-Schmid …
jorge vargas's user avatar
3 votes

Borel--Bott--Weil for the Grassmannians

Lars, search for a paper of Kostant ora paper of Griffiths-Schmid, you will find a complete answer to your question, even when \lambda is just an irreducible representation. best regards
jorge vargas's user avatar
1 vote

What are immediate applications of the classification of connected reductive groups?

check work of David Vogan, and a book of Trappa Vogan ...
jorge vargas's user avatar