Factor representations and their characters for the wreath products of compact groups with the infinite symmetric group
HIRAI, Takeshi Factor representations and their characters for the wreath products of compact groups with the infinite symmetric group. In: 表現論シンポジウム, 2005/11/15-18. (In Press)
November 2005: 表現論シンポジウム
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. The following text contains the part (1) and summaris of the parts (2) and (3).