Integrability of induction cocycles for Kac-Moody groups
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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.
Mathematics Subject Classification (2000)22F50 22E20 51E24 53C24 22E40 17B67
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