## Total positivity in the De Concini-Procesi Compactification

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- by Xuhua He
- Represent. Theory
**8**(2004), 52-71 - DOI: https://doi.org/10.1090/S1088-4165-04-00213-4
- Published electronically: April 21, 2004
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## Abstract:

We study the nonnegative part $\overline {G_{>0}}$ of the De Concini-Procesi compactification of a semisimple algebraic group $G$, 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. G.I. 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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## Bibliographic Information

**Xuhua He**- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- Email: hugo@math.mit.edu
- Received by editor(s): October 3, 2003
- Received by editor(s) in revised form: March 10, 2004
- Published electronically: April 21, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Represent. Theory
**8**(2004), 52-71 - MSC (2000): Primary 20G20; Secondary 14M15
- DOI: https://doi.org/10.1090/S1088-4165-04-00213-4
- MathSciNet review: 2048587