The regular and profinite representations of residually finite groups

Details The regular and profinite representations of residually finite groups The regular and profinite representations of residually finite groups

2012-04-06

arxiv.org/abs/1204.1514v1

Mathematics

Group Theory

19 pages, 1 figure

Scientific paper

Let $G$ be a residually finite group. To any decreasing sequence $\mathcal S = (H_n)_n $ of finite index subgroups of $G$ is associated a unitary representation $\rho_{\mathcal S}$ of $G$ in the Hilbert space $\bigoplus_{n=0}^{+\infty} \ell^2 (G/H_n) $. This paper investigates the following question: when does the representation $\rho_{\mathcal S} $ weakly contain the regular representation $\lambda$ of $G$?

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