We describe categorifications of 512 and braid groups. In a first part, we give a survey of the
case of 512 (joint work with Joseph Chuang [ChRou]) and explain how it leads to the …

We define and study sl_2-categorifications on abelian categories. We show in particular that
there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the …

The representation theory of symmetric groups is one of the most beautiful, popular, and
important parts of algebra with many deep relations to other areas of mathematics, such as …

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 present some topics of modular representation theory of finite groups, based on
functorial methods, and motivated by Broue's abelian defect group conjecture. In the first …

arXiv:math/0603356v2 [math.RT] 15 Mar 2006 Page 1 arXiv:math/0603356v2 [math.RT] 15 Mar
2006 Derived equivalences and finite dimensional algebras Raphaël Rouquier Abstract. We …

In this article we will give an overview of the new Lie theoretic approach to the p-modular
representation theory of the symmetric groups and their double covers that has emerged in …

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 odd analogs of results of Chuang and Rouquier on sl (2)-categorification.
Combined also with recent work of the second author with Livesey, this allows us to …

Given a categorical action of a Lie algebra, a celebrated theorem of Chuang and Rouquier
proves that the blocks corresponding to weight spaces in the same orbit of the Weyl group …