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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Total positivity in the De Concini-Procesi Compactification
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by Xuhua He PDF
Represent. Theory 8 (2004), 52-71 Request permission


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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Additional Information
  • Xuhua He
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Email:
  • 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:
  • MathSciNet review: 2048587