The University of Sydney
School of Mathematics and Statistics  
Algebra Seminar  
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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 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.