Capdeboscq, I. 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, 20(2), pp. 339-358. (doi: 10.4310/MRL.2013.v20.n2.a10)
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Publisher's URL: http://dx.doi.org/10.4310/MRL.2013.v20.n2.a10
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: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Thomas, Dr Anne |
Authors: | Capdeboscq, I., and Thomas, A. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Mathematics Research Letters |
Publisher: | International Press |
ISSN: | 1073-2780 |
ISSN (Online): | 1945-001X |
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