Lattices in complete rank 2 Kac–Moody groups
Capdeboscq, Inna (Korchagina) and Thomas, Anne. (2012) Lattices in complete rank 2 Kac–Moody groups. Journal of Pure and Applied Algebra, Vol.216 (No.6). pp. 1348-1371. ISSN 00224049Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.jpaa.2011.10.018
Let Λ be a minimal Kac–Moody group of rank 2 defined over the finite field Fq, where q=pa with p prime. Let G be the topological Kac–Moody group obtained by completing Λ. An example is , where K is the field of formal Laurent series over Fq. The group G acts on its Bruhat–Tits building X, a tree, with quotient a single edge. We construct new examples of cocompact lattices in G, many of them edge-transitive. We then show that if cocompact lattices in G do not contain p-elements, the lattices we construct are the only edge-transitive lattices in G, and that our constructions include the cocompact lattice of minimal covolume in G. We also observe that, with an additional assumption on p-elements in G, the arguments of Lubotzky (1990)  for the case may be generalised to show that there is a positive lower bound on the covolumes of all lattices in G, and that this minimum is realised by a non-cocompact lattice, a maximal parabolic subgroup of Λ.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Journal of Pure and Applied Algebra|
|Publisher:||Elsevier Science BV|
|Page Range:||pp. 1348-1371|
|Access rights to Published version:||Restricted or Subscription Access|
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