On the representations of the infinite symmetric group

Abstract

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.

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