Anne Thomas, University of Oxford and the University of Sydney

abstract:

A complete Kac-Moody group over a finite field is a totally disconnected locally compact group, which may be thought of as an infinite-dimensional Lie group. An example is G = SL(n,K) where K is the field of formal Laurent series over F_q. We consider lattices in such groups G of rank 2, and find a positive lower bound on the set of covolumes of cocompact lattices in G. We use finite group theory and the action of G on its associated Bruhat--Tits building, a tree. This is joint work with Inna (Korchagina) Capdeboscq.