Abstract

The  Broue-Malle-Michel  theory of spetses  associates to certain complex reflection groups combinatorially defined   data sets   whose properties   reflect   those of unipotent  characters   of   finite reductive groups.  On the other hand,  the Dwyer-Wilkerson  theory of  l-compact groups  associates to  l-adic   reflection groups  topological spaces  which possess much of the structure of compact  groups.   In this talk, I will discuss  how combining    spetsial  theory  with   the theory of l-compact groups    can be used to  define the  notion of the principal  block of    an  Z_l-spets    which  on a numerical  level conjecturally  resembles   the   principal  l-block  of a finite group. I will   present  some  supportive  evidence  which goes through a new  Yokonuma type  algebra   construction for torus normalisers  in l-compact groups.  This is joint work with  Gunter Malle and  Jason Semeraro.