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Harmonic analysis on the infinite symmetric group. A deformation of the regular representation. (English) Zbl 0796.43005
Let S(n) be the symmetric group of {1,2,,n} and S=S(n) the group of finite permutations of {1,2,}. The authors construct a family of unitary representations T z of S, parametrized by complex numbers z. These representations can be viewed as deformations of the regular T of S. They exhibit direct integral decompositions of these representations.

MSC:
43A65Representations of groups, semigroups, etc. (abstract harmonic analysis)
20C32Representations of infinite symmetric groups