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

中文翻译：

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量子反射群的拓扑生成和矩阵模型

我们为量子置换群$S^+_N$和量子反射群$H^{s+}_N$建立了几个新的拓扑生成结果。我们使用这些结果来表明这些量子群承认足够多的“矩阵模型”。特别是，所有这些量子群都具有残差有限离散对偶（尤其是超线性），并且 $S_N^+$ 的某些“平坦”矩阵模型是内在的。