University of Sydney Algebra Seminar
(University of Sydney)
Friday 9th December, 12.05-12.55pm, Carslaw 157
Rank polynomials revisited: a standard basis theorem for the Specht
modules of the general linear groups
The representation theory of the general linear groups in non-defining
characteristic has been shown to be closely related to that of the
symmetric groups Sn. In particular, one may define 'Specht modules'
whose properties are similar to those of the more tractable Specht
modules of Sn. In 2004, Gordon James
discussed an open problem in the
representation theory of the general linear groups, namely the problem
of defining a 'standard basis' for these Specht modules. This problem
has now been solved in the case that the Specht module is indexed by a
partition with 2 parts, though it remains open in general.