September 7-18,  2015

Through the work of Lusztig, it is known that the complex representations of a finite reductive group are controlled by a reflection group over Q (its Weyl group). In 1993, during a conference on the Greek island named Spetses, Broué, Malle and Michel observed that the reflection groups over Q could be replaced by certain complex reflection groups, now called spetsial groups ; certain numerical data (like the degrees of the unipotent irreducible representations) seem to be meaningful, although there is no reductive group around. This mysterious object is now called Spets, as a tribute to the eponymous island.

Work on Spetses (plural of Spets) has been the topics of several efficient working groups at CIRM. In particular, they made possible the publication of Split Spets for primitive reflection groups, Asterisque, 359, 1{146 (2014).

The aim of this two-week working group consists in
– extending the previous construction to the case of unsplit Spetses,
– generalizing to Spetses the theory of character sheaves,
– developing the computations of their Fourier matrices, and studying
their links with « fusion data »


Cédric Bonnafé (Université Montpellier 2)
Michel Broué (Université Paris Diderot)
Olivier Dudas (Université Paris Diderot)
Gunter Malle (
University of Kaiserslautern)
Jean Michel (
Université Paris Diderot)