On the representations of the infinite symmetric group

Mathematics – Representation Theory

Scientific paper

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My PhD thesis (1995). AMS TeX, 50 pages, 9 eps figures

Scientific paper

We classify all irreducible admissible representations of three Olshanski pairs connected to the infinite symmetric group. In particular, our methods yield two simple proofs of the classical Thoma's description of the characters of the infinite symmetric group. Also, we discuss a certain operation called mixture of representations which provides a uniform construction of all irreducible admissible representations.

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