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- W4288549836 abstract "Let $G$ be a countable group. We introduce several equivalence relations on the set ${rm Sub}(G)$ of subgroups of $G$, defined by properties of the quasi-regular representations $lambda_{G/H}$ associated to $Hin {rm Sub}(G)$ and compare them to the relation of $G$-conjugacy of subgroups. We define a class ${rm Sub}_{rm sg}(G)$ of subgroups (these are subgroups with a certain spectral gap property) and show that they are rigid, in the sense that the equivalence class of $Hin {rm Sub}_{rm sg}(G)$ for any one of the above equivalence relations coincides with the $G$-conjugacy class of $H$. Next, we introduce a second class ${rm Sub}_{rm w-par}(G)$ of subgroups (these are subgroups which are weakly parabolic in some sense) and we establish results concerning the ideal structure of the $C^*$-algebra $C^*_{lambda_{G/H}}(G)$ generated by $lambda_{G/H}$ for subgroups $H$ which belong to either one of the classes ${rm Sub}_{rm w-par}(G)$ and ${rm Sub}_{rm sg}(G)$. Our results are valid, more generally, for induced representations ${rm Ind}_H^G sigma$, where $sigma$ is a representation of $Hin {rm Sub}(G)$." @default.
- W4288549836 created "2022-07-29" @default.
- W4288549836 creator A5003113893 @default.
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- W4288549836 date "2019-03-01" @default.
- W4288549836 modified "2023-09-25" @default.
- W4288549836 title "Quasi-regular representations of discrete groups and associated C*-algebras" @default.
- W4288549836 doi "https://doi.org/10.48550/arxiv.1903.00202" @default.
- W4288549836 hasPublicationYear "2019" @default.
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