### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 813-867 |

Number of pages | 55 |

Journal | Communications in Contemporary Mathematics |

Volume | 5 |

Issue number | 5 |

DOIs | |

State | Published - Oct 1 2003 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Keywords

- Kac-Moody Lie algebra
- Kac-Moody group
- Lattices

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## Cite this

*Communications in Contemporary Mathematics*,

*5*(5), 813-867. https://doi.org/10.1142/S0219199703001117