Andrew Mathas (University of Sydney)

Gram matrices, gradings and simple modules.

Abstract:

The discovery of non-trivial Z-gradings on the group algebra of the symmetric group and related Hecke algebras has led to a flurry of activity. In this talk I will try to explain what the grading means in terms of the classical theory and how I think that the "new" combinatorics that comes with the grading should lead to dimension formulas for the graded simple modules and closed combinatorial formulas for the graded decomposition numbers.