Cocompact lattices in complete Kac-Moody groups with Weyl group right-angled or a free product of spherical special subgroups

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)

[img]
Preview
Text
83668.pdf

265kB

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
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
Related URLs:

University Staff: Request a correction | Enlighten Editors: Update this record