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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

4 votes
1 answer
309 views

How to write down the connection morphism in the long exact sequence in Čech cohomology expl...

Fix an integer $k$. Let $X=G/P$ be a complex rational homogeneous variety. I assume here $G$ is a simply connected semi simple complex Lie group and $P=P_k$ is a maximal parabolic subgroup defined by …
1 vote
1 answer
157 views

How to compute the index of a given weight?

I am learning the Borel–Weil–Bott theorem in rational homogeneous varieties. Working on them, I need to know two questions: How to judge if a weight is singular? How to compute the index of a given …