Subregular nilpotent representations of Lie algebras in prime characteristic

Jantzen, Jens

doi:10.1090/S1088-4165-99-00073-4

Subregular nilpotent representations of Lie algebras in prime characteristic
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by Jens Carsten Jantzen

Represent. Theory 3 (1999), 153-222

DOI: https://doi.org/10.1090/S1088-4165-99-00073-4

Published electronically: July 19, 1999

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Abstract:

We look in this paper at representations of Lie algebras of simple reductive groups in prime characteristic. We investigate those modules that have a subregular nilpotent $p$–character. In case all roots in the corresponding root system have the same length, we determine all simple modules in generic blocks as well as the Cartan matrices of these blocks. Our results confirm conjectures by Lusztig. We determine in these cases also extension groups between non-isomorphic simple modules. There are similar, somewhat less detailed results on non-generic blocks and the cases with two root lengths.

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