Abelian Unipotent Subgroups of Reductive Groups

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dc.creatorMcNinch, George J.
dc.date2000-07-10
dc.date2001-02-06
dc.date.accessioned2026-07-07T04:36:19Z
dc.date.available2026-07-07T04:36:19Z
dc.descriptionLet G be a connected reductive group defined over an algebraically closed field k of characteristic p > 0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the ``order formula'' of D. Testerman for unipotent elements in G; moreover, we show that the same formula determines the p-nilpotence degree of the corresponding nilpotent elements in the Lie algebra of G. Second, if G is semisimple and p is sufficiently large, we show that G always has a faithful representation (r,V) with the property that the exponential of dr(X) lies in r(G) for each p-nilpotent X in Lie(G). This property permits a simplification of the description given by Suslin, Friedlander, and Bendel of the (even) cohomology ring for the Frobenius kernels G_d, d > 1. The previous authors already observed that the natural representation of a classical group has the above property (with no restriction on p). Our methods apply to any Chevalley group and hence give the result also for quasisimple groups with ``exceptional type'' root systems. The methods give explicit sufficient conditions on p; for an adjoint semisimple G with Coxeter number h, the condition p > 2h -2 is always good enough.
dc.description27 pages; AMS LaTeX. This version fixes an error in section 7 (the fix makes the main result of section 9 true only under a condition on the prime). Moreover, it contains a number of changes in exposition
dc.identifierhttps://arxiv.org/abs/math/0007056
dc.identifierhttp://arxiv.org/abs/math/0007056
dc.identifierJournal of Pure and Applied Algebra 167 (2002) 269-300
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59552
dc.subjectRepresentation Theory
dc.titleAbelian Unipotent Subgroups of Reductive Groups
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