On the irreducibility of representations of measurable current groups
The main result is Theorem 4 in \S 8, which presents a necessary and sufficient condition (in terms of the cocycle \(r_x\)) for the irreducibility of the representations \[ \varphi\mapsto \exp (-|r(\varphi )|^2/2) T(\pi(\varphi), r(\varphi), -r(\varphi^{-1})) \] of the measurable current group \(G^x\) [cf. for example, \textit{H. Araki}, Publ. Res. Inst. Math. Sci., Kyoto Univ. 5 (1969), 361-422 (1970; Zbl 0238.22014), or \textit{K. R. Parthasarathy} and \textit{K. Schmidt}, Acta Math. 128, 53-71 (1972; Zbl 0233.22003)].
scientific article; zbMATH DE number 795613