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Representation Theory

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Subregular nilpotent representations of Lie algebras in prime characteristic

Author: Jens Carsten Jantzen
Journal: Represent. Theory 3 (1999), 153-222
MSC (1991): Primary 17B10; Secondary 17B20, 17B45, 17B50
Published electronically: July 19, 1999
MathSciNet review: 1703320
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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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Jens Carsten Jantzen
Affiliation: Matematisk Institut, Aarhus Universitet, Ny Munkegade, DK-8000 Aarhus C, Denmark

Received by editor(s): May 3, 1999
Received by editor(s) in revised form: June 9, 1999
Published electronically: July 19, 1999
Article copyright: © Copyright 1999 American Mathematical Society