Type: Seminar

Modified: Fri 2 Feb 2018 1510

Distribution: World

Expiry: 29 Mar 2018

CalTitle1: Algebra Seminar: On the Vershik-Kerov Conjecture Concerning Typical Dimensions of Representations of Finite Symmetric Groups

Auth: kevinc@pkevinc.pc (assumed)

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.