Michel Broué, Université de Paris VII (visiting MSRI)
Speculations about Spetses
Many features of the group GLn over a field with q elements, including its Sylow theory, character values, and modular representation theory, suggest that the group can be viewed as the specialization for x=q of a mysterious object, the corresponding `Spets'. The same applies to other reductive groups. Moreover, while the Weyl group of an actual reductive group must be a reflection group over Q, other reflection groups over the complex numbers apparently give rise to new Spetses. We shall present some evidence for these speculations.