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tag: algebraic-groups
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Steven Sam
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Steven Sam
  • 10.7k
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  • 80

Software for Borel-Weil-Bott in positive characteristic?

I am interested in calculating cohomology of line bundles on flag varieties $G/B$ in positive characteristic. But I really just have a bunch of scattered examples. Does there exist some kind of software that will calculate this for me? For the most part I don't care about the representation structure of the cohomology modules, I just want to know dimensions. Also, I know there are various results on when this cohomology is just like the char. 0 situation, but they won't always apply to my examples. So I don't need general results, just an algorithm.

I just know how to do one example using Macaulay2: irreducible homogeneous bundles on projective space (which are pushforwards of aforementioned line bundles). But I am also interested in things like type D, and homogeneous bundles on Grassmannians.