Open subgroups of locally compact Kac-Moody groups

Details Open subgroups of locally compact Kac-Moody groups Open subgroups of locally compact Kac-Moody groups

2011-08-24

arxiv.org/abs/1108.4934v1

Mathematics

Group Theory

23 pages, 1 figure

Scientific paper

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 has finite index in some parabolic subgroup. 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.

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