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A generalization of Steinbergs cross section

Xuhua He George Lusztig

Representation Theory mathscidoc:1912.43201

Journal of the American Mathematical Society, 25, (3), 739-757
Let G be a semisimple group over an algebraically closed field. Steinberg has associated to a Coxeter element G of minimal length G a subvariety G of G isomorphic to an affine space of dimension G which meets the regular unipotent class G in exactly one point. In this paper this is generalized to the case where G is replaced by any elliptic element in the Weyl group of minimal length G in its conjugacy class, G is replaced by a subvariety G of G isomorphic to an affine space of dimension G , and G is replaced by a unipotent class G of codimension G in such a way that the intersection of G and G is finite.
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@inproceedings{xuhuaa,
  title={A generalization of Steinbergs cross section},
  author={Xuhua He, and George Lusztig},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112917138834761},
  booktitle={Journal of the American Mathematical Society},
  volume={25},
  number={3},
  pages={739-757},
}
Xuhua He, and George Lusztig. A generalization of Steinbergs cross section. Vol. 25. In Journal of the American Mathematical Society. pp.739-757. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112917138834761.
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