Total positivity in the De Concini-Procesi Compactification

Author:
Xuhua He

Journal:
Represent. Theory **8** (2004), 52-71

MSC (2000):
Primary 20G20; Secondary 14M15

DOI:
https://doi.org/10.1090/S1088-4165-04-00213-4

Published electronically:
April 21, 2004

MathSciNet review:
2048587

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Abstract: We study the nonnegative part of the De Concini-Procesi compactification of a semisimple algebraic group , as defined by Lusztig. Using positivity properties of the canonical basis and parametrization of flag varieties, we will give an explicit description of . 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 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:
hugo@math.mit.edu

DOI:
https://doi.org/10.1090/S1088-4165-04-00213-4

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