This talk is an introduction as well as a survey about 2-representation theory of Coxeter groups.
Quite recently, Mazorchuk-Miemietz made very good progress towards a 'higher' analog of representations of finite-dimensional algebras (as e.g. groups rings of finite groups), and applied it successfully to one of the most well-behaved family of finite groups: finite Coxeter groups. Already in this case a lot of interesting new phenomena show up, most of which are neither present in classical representation theory, and which might lead to interesting connections and applications in the years to come.
Based on joint work with Marco Mackaay, Volodymyr Mazorchuk and Vanessa Miemietz.