University of Sydney Algebra Seminar

Oliver Ruff (University of Sydney)

Friday 14th October, 12.05-12.55pm, Carslaw 275

A (relatively) new approach to the representation theory of symmetric groups

I'll discuss the 1996 paper "A New Approach to the Representation Theory of Symmetric Groups" by Okounkov and Vershik (and/or their updated version from April of this year). In this paper the authors consider Gelfand-Tsetlin bases for modules over the symmetric group, and by analysing the spectra of the Jucys-Murphy elements they provide an elegant and mostly painless reconstruction of the ordinary representation theory of S_n. Part of the novelty of such an approach is that the branching rules are built into the theory from the outset, while the standard combinatorial objects only arise later on. Where appropriate, I'll also address the applicability of their methods to modular representation theory.