What can noncommutative probability tell about representation theory?

Claus Koestler (University College Cork)

Tuesday 29th October, 2013 16:00-17:00 Maths 416

Abstract

Among the principal motivations of von Neummann to introduce rings of operators, nowadays called von Neumann algebras, was the investigation 
of unitary representations of large groups.  A prototype of such a large group is the group of all finite permutations.  Its extreme characters had 
been characterized by Thoma in the 1960s, and alternative proofs have been given by Vershik & Kerov in the 1980s, as well as by Okounkov 
around 1995.  But none of these proofs uses really an operator algebraic toolkit.  Recently we have found a new purely operator algebraic proof 
of Thoma's theorem which shows that Thoma's theorem is actually a noncommutative de Finetti theorem.  
My talk will introduce into related new developments and is based in parts on joint work with Rolf Gohm.

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