One of the amazing developments of the last decade is the discovery that the actions of certain restriction and induction operators on the totality of all blocks of the symmetric groups induce an action of the Chevalley generators of an affine Lie algebra on the Grothendieck group, represented by an object imported from physics called the crystal graph. The theory extends naturally to Hecke algebras. The cases where the underlying parameter is generic or a root of unity are usually treated as distinct cases, but a brand new result of Hu and Mathas on the existence of a graded cellular basis demonstrates the importance of viewing the blocks at roots of unity as having deformations to separable algebras.
Deformation Theory Seminar
Wednesday, December 9, 2009 - 2:00pm
Prof. Malka Schaps
Bar-Ilan University