Capdeboscq, Inna (Korchagina) and Thomas, A. (2013) Cocompact lattices in complete kac-moody groups with weyl group right-angled or a free product of spherical special subgroups. Mathematics Research Letters, Volume 20 (Number 2). pp. 339-358. doi:10.4310/MRL.2013.v20.n2.a10 ISSN 1073-2780.

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Abstract

Let G be a complete Kac-Moody group of rank n \geq 2 over the finite field of order q, with Weyl group W and building \Delta. We first show that if W is right-angled, then for all q \neq 1 mod 4 the group G admits a cocompact lattice \Gamma which acts transitively on the chambers of \Delta. We also obtain a cocompact lattice for q =1 mod 4 in the case that \Delta is Bourdon's building. As a corollary of our constructions, for certain right-angled W and certain q, the lattice \Gamma has a surface subgroup. We also show that if W is a free product of spherical special subgroups, then for all q, the group G admits a cocompact lattice \Gamma with \Gamma a finitely generated free group. Our proofs use generalisations of our results in rank 2 concerning the action of certain finite subgroups of G on \Delta, together with covering theory for complexes of groups.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Mathematics Research Letters
Publisher:	Mathematical Publishing
ISSN:	1073-2780
Official Date:	2013
Dates:	Date Event 2013 Published
Volume:	Volume 20
Number:	Number 2
Page Range:	pp. 339-358
DOI:	10.4310/MRL.2013.v20.n2.a10
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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