By Benjamin Brück and others at

University of Muenster

and Westfälische Wilhelms-Universität Münster

We construct explicit finite-dimensional orthogonal representations *\pi_N* of *\operatorname{SL}_{N}(\mathbb{Z})* for *N \in \{3,4\}* all of whose invariant vectors are trivial, and such that *H^{N - 1}(\operatorname{SL}_{N}(\mathbb{Z}),\pi_N)* is non-trivial. This implies that for *N* as above, the group *\operatorname{SL}_{N}(\mathbb{Z})* does not have property *(T_{N-1})* of Bader-Sauer and therefore is not *(N-1)*-Kazhdan... Show more

October 30, 2024

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