University of Sydney Algebra Seminar

Alexander Bufetov (Institut de mathematiques Marseille)

Friday 16 February, 12-1pm, Place: Carslaw 375

On the Vershik-Kerov Conjecture Concerning Typical Dimensions of Representations of Finite Symmetric Groups

Vershik and Kerov conjectured in 1985 that suitably normalized dimensions of irreducible representations of finite symmetric groups converge to a constant with respect to the Plancherel family of measures on the space of Young diagrams. They proposed to call the resulting constant the entropy of the Plancherel measure and to view the conjectured result as the analogue of the Shannon-Macmillan-Breiman theorem in this context. The main result of the talk is the proof of the Vershik-Kerov conjecture. The argument relies on the methods of Borodin, Okounkov and Olshanski.