Total positivity in the De Concini-Procesi Compactification

He, Xuhua

doi:10.1090/S1088-4165-04-00213-4

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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