Is it possible to prove the Borel-Weil-Bott theorem without learning complex analysis? Is it recommended?
I know sheaf cohomology, representation theory, vector bundles and some tools of Lie group theory, but I do not know much about holomorphic bundles. Can I learn these without learning some serious complex analysis?
Reason: I find the complex analysis stuff that I see in textbooks very boring and I find myself working through it extremely slowly in comparison to other more familiar topics - I don't know if I have the time to really trudge through it in regard to my study planning.
If I do indeed need to learn complex analysis, what would I need? I need to know, in order to determine if I have time in the near future to even look at this.