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Total positivity in the De Concini-Procesi Compactification

Author: Xuhua He
Journal: Represent. Theory 8 (2004), 52-71
MSC (2000): Primary 20G20; Secondary 14M15
Published electronically: April 21, 2004
MathSciNet review: 2048587
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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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Xuhua He
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Received by editor(s): October 3, 2003
Received by editor(s) in revised form: March 10, 2004
Published electronically: April 21, 2004
Article copyright: © Copyright 2004 American Mathematical Society