Let g be a Kac-Moody Lie algebra. We give an interpretation of Tits' associated group functor using representation theory of 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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Kac-Moody Lie algebra
- Kac-Moody group