Existence of lattices in Kac-Moody groups over finite fields

Lisa Carbone, Howard Garland

Research output: Contribution to journalArticle

28 Scopus citations

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 languageEnglish (US)
Pages (from-to)813-867
Number of pages55
JournalCommunications in Contemporary Mathematics
Volume5
Issue number5
DOIs
StatePublished - 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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