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Tagged with flag-varieties kahler-manifolds
3 questions
9
votes
2
answers
963
views
Hard Lefschetz Theorem for the Flag Manifolds
In the case of a generalized flag manifold $G/P$, we have an explicit description of their cohomology groups due to Borel.(See herehere for a description.) I would like to know what the hard Lefschetz ...
6
votes
1
answer
275
views
Equivariant Almost Complex Structures on the Full Flag Manifolds
On complex projective space ${\bf CP}^m$, there exists a unique $SU(m+1)$-equivariant almost-complex structure. What happens for the case of the full flag manifold of $SU(m+1)$, which is to say the ...
6
votes
1
answer
516
views
Lagrangian Grassmannian as a Spin Manifold
I am trying to better understand this nice answer to a question of mine, which states
Spin structures on a compact complex manifold $(M^{2n},J)$ are in bijective correspondence with isomorphism ...