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Unipotent variety in the group compactification

Xuhua He

Representation Theory mathscidoc:1912.43198

Advances in Mathematics, 203, (1), 109-131, 2006.6
The unipotent variety of a reductive algebraic group G plays an important role in the representation theory. In this paper, we will consider the closure U of the unipotent variety in the De ConciniProcesi compactification G of a connected simple algebraic group G. We will prove that U-U is a union of some G-stable pieces introduced by Lusztig in [Moscow Math. J 4 (2004) 869896]. This was first conjectured by Lusztig. We will also give an explicit description of U. It turns out that similar results hold for the closure of any Steinberg fiber in G.
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@inproceedings{xuhua2006unipotent,
  title={Unipotent variety in the group compactification},
  author={Xuhua He},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112905737425758},
  booktitle={Advances in Mathematics},
  volume={203},
  number={1},
  pages={109-131},
  year={2006},
}
Xuhua He. Unipotent variety in the group compactification. 2006. Vol. 203. In Advances in Mathematics. pp.109-131. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112905737425758.
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