Irreducibility In Algebraic Groups And Regular Unipotent Elements

We study (connected) reductive subgroups G of a reductive algebraic group H, where G contains a regular unipotent element of H. The main result states that G cannot lie in a proper parabolic subgroup of H. This result is new even in the classical case H = SL(n, F), the special linear group over an algebraically closed field, where a regular unipotent element is one whose Jordan normal form consists of a single block. In previous work, Saxl and Seitz (1997) determined the maximal closed positive-dimensional (not necessarily connected) subgroups of simple algebraic groups containing regular unipotent elements. Combining their work with our main result, we classify all reductive subgroups of a simple algebraic group H which contain a regular unipotent element.


Published in:
Proceedings Of The American Mathematical Society, 141, 1, 13-28
Year:
2013
Publisher:
Providence, Amer Mathematical Soc
ISSN:
0002-9939
Laboratories:




 Record created 2013-12-09, last modified 2018-03-17


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