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We establish several new topological generation results for the quantumpermutation groups $S^+_N$ and the quantum reflection groups $H^{s+}_N$. We usethese results to show that these quantum groups admit sufficiently many "matrixmodels". In particular, all of these quantum groups have residually finitediscrete duals (and are, in particular, hyperlinear), and certain "flat" matrixmodels for $S_N^+$ are inner faithful.

Topological generation and matrix models for quantum reflection groups