Abelian unipotent subgroups of reductive groups

@article{McNinch2000AbelianUS,
  title={Abelian unipotent subgroups of reductive groups},
  author={George J. McNinch},
  journal={Journal of Pure and Applied Algebra},
  year={2000},
  volume={167},
  pages={269-300}
}
  • George J. McNinch
  • Published 10 July 2000
  • Mathematics
  • Journal of Pure and Applied Algebra
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37 Citations
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37 Citations

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References

SHOWING 1-10 OF 31 REFERENCES

On some simple groups defined by C. Chevalley

Introduction. For any semi-simple Lie algebra g over the field of complex numbers and an arbitrary field K, C. Chevalley [2] defined a group © by a uniform method. The group © turns out to be simple…

An analogue of the Jacobson-Morozov theorem for Lie algebras of reductive groups of good characteristics

Let g be the Lie algebra of a connected reductive group G over an algebraically closed field of characteristic p > 0. Suppose that G(1) is simply connected and p is good for the root system of G.…

Witt groups and unipotent elements in algebraic groups

Let G be a semisimple algebraic group defined over an algebraically closed field K of good characteristic p>0. Let u be a unipotent element of G of order pt, for some t ∈ N. In this paper it is shown…

Support varieties for infinitesimal group schemes

The representation theory of a connected smooth affine group scheme over a field k of characteristic p > 0 is faithfully captured by that of its family of Frobenius kernels. Such FRobenius kernels…

Unipotent elements, tilting modules, and saturation

The results in this paper were motivated by work of Serre [19] where semisimplicity results for representations of arbitrary groups in positive characteristic were established. A key ingredient in…

Infinitesimal 1-parameter subgroups and cohomology

This is the first of two papers in which we determine the spectrum of the cohomology algebra of infinitesimal group schemes over a field k of characteristic p > 0. Whereas [SFB] is concerned with…

Finite groups of Lie type

Frobenius splitting of cotangent bundles of flag varieties

We use the G-invariant non-degenerate form on the Steinberg module to Frobenius split the cotangent bundle of a flag variety in good prime characteristics. This was previously only known for the…

Conjugacy classes in semisimple algebraic groups

Review of semisimple groups Basic facts about classes and centralizers Centralizers of semisimple elements The adjoint quotient Regular elements Parabolic subgroups and unipotent classes The…

Finite groups of Lie type: Conjugacy classes and complex characters

BN-Pairs and Coxeter Groups. Maximal Tori and Semisimple Classes. Geometric Conjugacy and Duality. Unipotent Classes. The Steinberg Character. The Generalized Characters of Deligne-Lusztig. Further…