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

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

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 -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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Additional Information

**Jens Carsten Jantzen**

Affiliation:
Matematisk Institut, Aarhus Universitet, Ny Munkegade, DK-8000 Aarhus C, Denmark

Email:
jantzen@imf.au.dk

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

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