2.00 pm, Lecture Hall 2
A new approach to the representation theory of the infinite symmetric group
University College Cork Ireland.
The infinite symmetric group is the group of all finite permutations and a paradigm for a 'wild' group.
Its extremal characters are characterized by the famous Thoma theorem and Vershik & Kerov, Okounkov, Olshanski and many others have developed its representation theory during the past decades. Recently we have found a new operator algebraic proof of the Thoma theorem, identifying it as a noncommutative de Finetti theorem.
My talk will introduce to these recent developments and is based in parts on joint work with Gwion Evans and Rolf Gohm.