Unipotent variety in the group compactification

Details Unipotent variety in the group compactification Unipotent variety in the group compactification

2004-10-07

arxiv.org/abs/math/0410199v3

Mathematics

Representation Theory

21 pages. Final version. To appear in Adv. in Math

Scientific paper

The unipotent variety of a reductive algebraic group $G$ plays an important role in the representation theory. In this paper, we will consider the closure $\bar{\Cal U}$ of the unipotent variety in the De Concini-Procesi compactification $\bar{G}$ of a connected simple algebraic group $G$. We will prove that $\bar{\Cal U}-\Cal U$ is a union of some $G$-stable pieces introduced by Lusztig in \cite{L4}. This was first conjectured by Lusztig. We will also give an explicit description of $\bar{\Cal U}$. It turns out that similar results hold for the closure of any Steinberg fiber in $\bar{G}$.

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