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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.

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
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