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• W1836042012 abstract "We prove that connected higher rank simple Lie groups have Lafforgue's strong property (T) with respect to a certain class of Banach spaces $mathcal{E}_{10}$ containing many classical superreflexive spaces and some non-reflexive spaces as well. This generalizes the result of Lafforgue asserting that $mathrm{SL}(3,mathbb{R})$ has strong property (T) with respect to Hilbert spaces and the more recent result of the second named author asserting that $mathrm{SL}(3,mathbb{R})$ has strong property (T) with respect to a certain larger class of Banach spaces. For the generalization to higher rank groups, it is sufficient to prove strong property (T) for $mathrm{Sp}(2,mathbb{R})$ and its universal covering group. As consequences of our main result, it follows that for $X in mathcal{E}_{10}$, connected higher rank simple Lie groups and their lattices have property (F$_X$) of Bader, Furman, Gelander and Monod, and that the expanders contructed from a lattice in a connected higher rank simple Lie group do not admit a coarse embedding into $X$." @default.
• W1836042012 created "2016-06-24" @default.
• W1836042012 creator A5029748695 @default.
• W1836042012 creator A5082630604 @default.
• W1836042012 date "2015-09-09" @default.
• W1836042012 modified "2023-10-14" @default.
• W1836042012 title "Strong property (T) for higher-rank simple Lie groups: Figure 1." @default.
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• W1836042012 doi "https://doi.org/10.1112/plms/pdv040" @default.
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