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Vertices of simple modules for the symmetric and related finite groups (D07.SymGps.Ox)
Start date: 31 Jul 2009, End date: 30 Jul 2011 PROJECT  FINISHED 

This project aims to study representations of symmetric groups, alternating groups and other related finite groups, over non-zero characteristic. These representations are far from being semisimple, and many basic problems, like finding the irreducible representations - that is simple modules - are not solved in general. Therefore one needs to find and understand invariants of modules. We will focus on the distiguished classes of Specht modules and simple modules and will investigate vertices, sources, and complexity. These encapsulate local and group theoretic features on the one hand, and large-scale homological behaviour on the other hand. Spectacular new developments from Lie theory have opened up completely new perspectives, and we will combine the classical approach of G.D. James, the new methods originating in Kac-Moody algebras and quantum groups, and work by Kleshchev , Lascoux/Leclerc/Thibon, Ariki, Grojnowski, and Chuang/Rouquier.
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