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<p>We prove that relatively hyperbolic groups do not have Lafforgue strong property (<i>T</i>) with respect to Hilbert spaces. To do so we construct an unbounded affine representation of such groups, whose linear part is of polynomial growth of degree 2. Moreover, this representation is proper for the metric of the coned-off graph.</p>

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Strong property (T) and relatively hyperbolic groups

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • Hermès Lajoinie-Dodel

摘要

We prove that relatively hyperbolic groups do not have Lafforgue strong property (T) with respect to Hilbert spaces. To do so we construct an unbounded affine representation of such groups, whose linear part is of polynomial growth of degree 2. Moreover, this representation is proper for the metric of the coned-off graph.