The classification of the finite simple groups is considered as one of the greatest
achievements in mathematics of the twentieth century. The result provides the most basic …

The representation theory of finite groups has, at its core, a collection of open problems.
Taken together, they are called 'local-global conjectures', although 'localglobal rough …

We survey some fundamental trends in representation theory of symmetric groups and
related objects which became apparent in the last fifteen years. The emphasis is on …

We prove Erdmann's conjecture (J Algebra 76: 505–518, 1982) stating that every block with
a Klein four defect group has a simple module with trivial source, and deduce from this that …

Given a dihedral 2-group P of order at least 8, we classify the splendid Morita equivalence
classes of principal 2-blocks with defect groups isomorphic to P. To this end we construct …

We define and study RoCK blocks for double covers of symmetric groups. We prove that
RoCK blocks of double covers are Morita equivalent to standardlocal'blocks. The analogous …

We calculate the (super) decomposition matrix for a RoCK block of a double cover of the
symmetric group with abelian defect, verifying a conjecture of the first author. To do this, we …

To what extent does the defect group of a block determine its structure and that of its module
category? More specifically, how are certain invariants associated to a block controlled by its …

We compare the canonical bases of level-1 quantised Fock spaces in affine types A (1) and
A (2), showing how to derive the canonical basis in type A(2) 2n from the the canonical basis …

This article contains reduction theorems for some weaker variants of Donovan's conjecture,
which supposes that, for every finite group D of prime order p, there are only finitely many …