Total positivity in the De Concini-Procesi compactification
Representation Theory
2007-05-23 v2
Abstract
We study the nonnegative part \bar{G_{>0}} of the De Concini-Procesi compactification of a reductive 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 \bar{G_{>0}}. This answers the question of Lusztig in [L4]. We will also prove that \bar{G_{>0}} has a cell decomposition which was conjectured by Lusztig.
Cite
@article{arxiv.math/0310031,
title = {Total positivity in the De Concini-Procesi compactification},
author = {Xuhua He},
journal= {arXiv preprint arXiv:math/0310031},
year = {2007}
}
Comments
23 pages. Some corrections. References updated