University of Sydney Algebra Seminar
(University of Sydney)
Friday 14th October, 12.05-12.55pm, Carslaw 275
A (relatively) new approach to the representation theory of
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 Sn.
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.