Semigroup approach to representation theory of infinite wreath products
Yun S. Yoo, Robert Paul Boyer · 2010
We consider the group S(1) of all permutations of the set of naturals, N, with topology of pointwise convergence. Lieberman proved that any representation T of the S(1) is a direct sum of irreducible representations; in particular, T generates a von Neumann algebra of type I. Lieberman's proof is very complicated and can hardly be applied to more general semigroups. Olshanski found another proof of Lieberman's theorem based on semigroup approach. Using this approach we extend the Lieberman's Theorem on the case of the wreath product of S(1) with Z2 endowed with the topology of pointwise convergence.