Algebra Seminar: Bufetov -- On the Vershik-Kerov Conjecture Concerning Typical Dimensions of Representations of Finite Symmetric Groups

Alexander Bufetov (Institut de mathematiques Marseille) 

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

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

Abstract: 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.