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 Lp 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.
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Prépublication de l’Institut Fourier nº 637 (2004); e-mail: http://www-fourier.ujf-grenoble.fr/prepublicatons.html
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Rémy, B. Integrability of induction cocycles for Kac-Moody groups. Math. Ann. 333, 29–43 (2005). https://doi.org/10.1007/s00208-005-0663-1
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DOI: https://doi.org/10.1007/s00208-005-0663-1