Connected components of real double Bruhat cells
摘要
Double Bruhat cells in a semisimple group are intersections of cells in two Bruhat decompositions corresponding to two opposite Borel subgroups. They form a geometric framework for the study of total positivity in semisimple groups; they are also closely related to symplectic leaves in the corresponding Poisson-Lie groups. The term "cells" might be misleading because their topology can be quite non-trivial. As a first step towards understanding this topology, we enumerate the connected components of real double Bruhat cells. This result extends (from the simply-laced case to the general one) and proves the conjecture made in a joint work with B.Shapiro-M.Shapiro-A.Vainshtein; it also extends earlier work by B.Shapiro-M.Shapiro-A.Vainshtein and K.Rietsch.
引用
@article{arxiv.math/0003231,
title = {Connected components of real double Bruhat cells},
author = {Andrei Zelevinsky},
journal= {arXiv preprint arXiv:math/0003231},
year = {2007}
}
备注
18 pages, 4 figures; the title corrected, the abstract slightly modified, one reference added, the proof of Lemma 4.4 simplified