Total positivity in the De Concini-Procesi compactification

Details Total positivity in the De Concini-Procesi compactification Total positivity in the De Concini-Procesi compactification

2003-10-02

arxiv.org/abs/math/0310031v2

Mathematics

Representation Theory

23 pages. Some corrections. References updated

Scientific paper

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.

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