Open subgroups of locally compact Kac-Moody groups
Group Theory
2013-02-21 v2
Abstract
Let G be a complete Kac-Moody group over a finite field. It is known that G possesses a BN-pair structure, all of whose parabolic subgroups are open in G. We show that, conversely, every open subgroup of G is contained with finite index in some parabolic subgroup; moreover there are only finitely many such parabolic subgroups. The proof uses some new results on parabolic closures in Coxeter groups. In particular, we give conditions ensuring that the parabolic closure of the product of two elements in a Coxeter group contains the respective parabolic closures of those elements.
Cite
@article{arxiv.1108.4934,
title = {Open subgroups of locally compact Kac-Moody groups},
author = {Pierre-Emmanuel Caprace and Timothée Marquis},
journal= {arXiv preprint arXiv:1108.4934},
year = {2013}
}
Comments
Minor changes. Theorem A has been slightly improved and now contains an additional finiteness statement