Dudko, A. V.; Nessonov, N. I. Characters of projective representations of the infinite generalized symmetric group. (English. Russian original) Zbl 1185.20013 Sb. Math. 199, No. 10, 1421-1450 (2008); translation from Mat. Sb. 199, No. 10, 3-32 (2008). Summary: By the infinite generalized symmetric group we mean the group \(B_m=\mathfrak S_\infty\ltimes\mathbb{Z}_m^\infty\), where \(\mathbb{Z}_m^\infty\) is the group of all sequences \(\{z_k\}_{k=1}^\infty\) in \(\mathbb{Z}_m\) containing only finitely many non-zero elements \(z_k\) and \(\mathfrak S_\infty\) is the group of all finitely supported permutations of the positive integers. A complete description of the projective factor representations of \(B_m\) of finite type is obtained. Cited in 1 Document MSC: 20C32 Representations of infinite symmetric groups 20C25 Projective representations and multipliers 22D10 Unitary representations of locally compact groups 22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations 46L10 General theory of von Neumann algebras Keywords:projective representations; infinite generalized symmetric group; indecomposable characters; covering groups PDFBibTeX XMLCite \textit{A. V. Dudko} and \textit{N. I. Nessonov}, Sb. Math. 199, No. 10, 1421--1450 (2008; Zbl 1185.20013); translation from Mat. Sb. 199, No. 10, 3--32 (2008) Full Text: DOI