University of Birmingham, Wednesday January 20th, 2016
All talks will be held in LRA of the Watson building on the main campus of the University of Birmingham, whilst welcome and registration will be held in the Common Room on the Second Floor of the same building. Directions here.
The Morita Frobenius number of an algebra is the number of Morita equivalence classes of its Frobenius twists. They were first introduced by Kessar in 2004 the context of Donovan’s conjecture. I will present results in ongoing work in which we aim to calculate the Morita Frobenius numbers of all blocks of group algebras of quasi-simple finite groups.
In 2008, Brundan, Kleshchev and Wang showed that Specht modules over cyclotomic Hecke algebras are gradable. Firstly, I will discuss the grading on these modules together with results on graded dimensions of certain Specht modules, in particular, those indexed by hook partitions. Using these formulae, I will then discuss an alternative proof of Chuang, Miyachi and Tan’s result on the graded decomposition numbers of these particular Specht modules in level 1. Finally, I will give an overview of my current work, in which I am using an analogous approach to obtain the (graded) decomposition numbers of a particular set of Specht modules in level 2.
Advances in our understanding of blocks of finite groups of Lie type raise the possibility of classifying blocks with certain defect groups for the prime two. I will survey some of the methods involved, as well as some recent results.