Abstract
Let
${\mathfrak g}$
be a Kac–Moody Lie algebra. We give an interpretation
of Tits' associated group functor using representation theory of
${\mathfrak g}$
and we construct a locally compact "Kac–Moody group" G
over a finite field k. Using (twin) BN-pairs (G,B,N) and
(G,B-,N) for G we show that if k
is "sufficiently large", then the subgroup B-
is a non-uniform lattice in G. We have also constructed an
uncountably infinite family of both uniform and non-uniform
lattices in rank 2. We conjecture that these form
uncountably many distinct conjugacy classes in G. The basic tool for
the construction of non-uniform lattices in rank 2 is a spherical Tits
system for G which we also construct.