Basic Set and Perfect Isometries
May 30 – June 10, 2016
This project is concerned with the modular representation theory of finite groups. One of the fundamental questions in p-modular representation theory is that of finding the p-decomposition matrix of the group. To tackle this extremely hard question, which is still open for many finite groups, such as for example the symmetric groups, one strategy is to find a p-basic set of the group. However, to this date, the existence of p-basic sets has still not been proven for the double covers of the symmetric or alternating groups. This is one of the main questions that we will consider in this project.
Furthermore, in recent works, we prove that there is a strong link between p-basic sets and p-perfect isometries (in the sense of Broué or Kulshammer-Olsson-Robinson).We aim to construct perfect isometries between some p-blocks of complex refection groups of the infinite serie.

Olivier Brunat (Université Paris Diderot)
Jean-Baptiste Gramain (University of Aberdeen)