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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the generic structure of cohomology modules for semisimple algebraic groups


Author: Henning Haahr Andersen
Journal: Trans. Amer. Math. Soc. 295 (1986), 397-415
MSC: Primary 20G05; Secondary 20G10
DOI: https://doi.org/10.1090/S0002-9947-1986-0831206-2
MathSciNet review: 831206
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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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DOI: https://doi.org/10.1090/S0002-9947-1986-0831206-2
Article copyright: © Copyright 1986 American Mathematical Society