Factor representations and their characters for the wreath products of compact groups with the infinite symmetric group

TL;DRAbstract

Let T be a compact group, and denote by G = G_∞(T) the wreath product of T with the infinite symmetric group G_∞. (1) We study first characters of facter representations of finite type of G and give a general character formula. (2) Then, for each character f, we give a realization of a factor representation π corresponding to it with a trace-element v such that f(g) = <π(g)v, v>. (3) Further we study limits of irreducible characters of Gn = Sn(T) as n → ∞, and show that all the characters are obtained as such limits.\n\nThe following text contains the part (1) and summaris of the parts (2) and (3).

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