On representations of the infinite symmetric group

A. Okounkov

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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

Original languageEnglish
Pages (from-to)3550-3589
Number of pages40
JournalJournal of Mathematical Sciences
Issue number5
Publication statusPublished - 1999
Externally publishedYes


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