A20: Towards unipotent character sheaves associated to Coxeter groups

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.