Irreducible induced representations of ICC-groups
Let \(G\) be an ICC-group, i.e. \(G\) is discrete and the regular representation \(\lambda\) is a factor representation; and let \(H\) be an abelian subgroup. We study the direct integral decomposition \(\lambda=\int^ \oplus_{\widehat H}\text{ind}^ G_ H\sigma d\mu(\sigma)\) in order to find representations that are induced from finite-dimensional ones and that are irreducible as well as weakly equivalent to \(\lambda\). One section is devoted to the infinite symmetric group, where non-abelian subgroups are needed to obtain those representations. Moreover an example of a maximal abelian direct integral decomposition of a factor representation into reducible fibres is given.
scientific article; zbMATH DE number 126354
scientific article