Some decades ago, it has been noticed that key invariants in the representation theory of finite reductive groups, like unipotent characters and Fourier transform matrices, seem to have a life beyond reductive groups: they can be associated to non-crystallographic Coxeter groups as well, even though there is no reductive group anymore. The goal of this project is to investigate a recent conjecture by Lusztig which would explain this phenomenon from a higher, i.e. categorical, point of view using the theory of Soergel bimodules. Part of the project will be the implementation of the relevant categories in the computer.
