On the generic structure of cohomology modules for semisimple algebraic groups

Andersen, Henning Haahr

doi:10.1090/S0002-9947-1986-0831206-2

On the generic structure of cohomology modules for semisimple algebraic groups
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Trans. Amer. Math. Soc. 295 (1986), 397-415 Request permission

Abstract:

Let $G$ be a connected semisimple algebraic group over a field of positive characteristic. Denote by $B$ a Borel subgroup. Our main result says that generically the cohomology modules for line bundles on $G/B$ have simple socles and simple heads, and we identify the corresponding highest weights. As one of the consequences we discover a certain symmetry among extensions of simple modules for $G$.

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Cohomology of

characteristic

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