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Actions of higher rank groups on uniformly convex Banach spaces

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arxiv 2303.01405 v2 pith:HA4QN5WW submitted 2023-03-02 math.GR math.FA

Tim de Laat , Mikael de la Salle This is my paper · ORCID
classification math.GRmath.FA
keywords higherrankbanachgroupsactionsconvexsimplespaces
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We prove that all isometric actions of higher rank simple Lie groups and their lattices on arbitrary uniformly convex Banach spaces have a fixed point. This vastly generalises a recent breakthrough of Oppenheim. Combined with earlier work of Lafforgue and of Liao on strong Banach property (T) for non-Archimedean higher rank simple groups, this confirms a long-standing conjecture of Bader, Furman, Gelander and Monod. As a consequence, we deduce that sequences of Cayley graphs of finite quotients of a higher rank lattice are super-expanders.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Geometric Banach property (T) for metric spaces via Banach representations of Roe algebras

    math.FA 2025-05 conditional novelty 8.0 of 10

    Geometric Banach property (T) is defined via Banach representations of Roe algebras, shown to be coarsely invariant, equivalent to Kazhdan projections in Banach-Roe algebras, and linked to Banach property (T) of limit...

  2. Discrete Poincar\'e inequalities and universal approximators for random graphs

    math.MG 2025-06 conditional novelty 7.0 of 10

    Independent random regular graphs satisfy a dimension-free nonlinear Poincaré inequality, resolving Kleinberg's problem and giving universal approximators for all p ≥ 1.

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