Ulrich Thiel

Cuspidal Calogero-Moser and Lusztig families for finite Coxeter groups

Abstract:

A fundamental tool in studying the (ordinary) representation theory of a finite group of Lie type is the partition of the (ordinary) irreducible characters of the corresponding Weyl group into so-called Lusztig families. The most important families are the cuspidal ones, which are those not induced from a proper parabolic subgroup. In joint work with Gwyn Bellamy (University of Glasgow) we have identified these families as being the zero-dimensional symplectic leaves of the Calogero-Moser space attached to the Weyl group, thus providing a Poisson geometric interpretation of Lusztigâ€™s notion of cuspidality. This is further evidence for a fundamental (yet unknown) connection between finite groups of Lie type and rational Cherednik algebras at t=0.