University of Sydney Algebra Seminar

Sinéad Lyle (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 S_n. In particular, one may define 'Specht modules' whose properties are similar to those of the more tractable Specht modules of S_n. 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.