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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 ...
Falertu Vatilski's user avatar
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 ...
Christian Fischmann's user avatar
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 ...
Janos Erdmann's user avatar