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Total positivity in the De Concini-Procesi compactification

Xuhua He

Representation Theory mathscidoc:1912.43224

Representation Theory of the American Mathematical Society, 8, (3), 52-71, 2004
We study the nonnegative part \overline {G_ {> 0}} of the De Concini-Procesi compactification of a semisimple algebraic group \overline {G_ {> 0}} , as defined by Lusztig. Using positivity properties of the canonical basis and parametrization of flag varieties, we will give an explicit description of \overline {G_ {> 0}} . This answers the question of Lusztig in Total positivity and canonical bases, Algebraic groups and Lie groups (ed. GI Lehrer), Cambridge Univ. Press, 1997, pp. 281-295. We will also prove that \overline {G_ {> 0}} has a cell decomposition which was conjectured by Lusztig.
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@inproceedings{xuhua2004total,
  title={Total positivity in the De Concini-Procesi compactification},
  author={Xuhua He},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113036811025784},
  booktitle={Representation Theory of the American Mathematical Society},
  volume={8},
  number={3},
  pages={52-71},
  year={2004},
}
Xuhua He. Total positivity in the De Concini-Procesi compactification. 2004. Vol. 8. In Representation Theory of the American Mathematical Society. pp.52-71. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113036811025784.
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