Fourier matrices and character sheaves


The general topic of the project is Lusztig’s geometric theory of representations of finite groups of Lie type. Specific aims: Develop algorithms for systematic experiments with Lusztig’s abstract definition of Fourier matrices. Establish new instances of Lusztig’s conjecture on character sheaves and almost characters for groups with disconnected center. In particular, explicit determination of decompositions of characteristic functions of all cuspidal character sheaves into irreducible characters.