, Volume 333, Issue 1, pp 29-43
Date: 14 Jun 2005

Integrability of induction cocycles for Kac-Moody groups

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Abstract

We prove that whenever a Kac-Moody group over a finite field is a lattice of its buildings, it has a fundamental domain with respect to which the induction cocycle is L p for any p ∈ [1;+∞). The proof uses elementary counting arguments for root group actions on buildings. The applications are the possibility to apply some lattice superrigidity, and the normal subgroup property for Kac-Moody lattices.

Prépublication de l’Institut Fourier nº 637 (2004); e-mail: http://www-fourier.ujf-grenoble.fr/prepublicatons.html