2007-09-28
Richard Vale, Cornell University
The almost-semisimple Ariki-Koike algebra
In this talk, we consider a finite complex reflection group W and two
interesting algebras associated to W. One is the cyclotomic Hecke algebra,
which is a deformation of the group algebra of W, depending on some
parameters. The other is the Cherednik algebra, which is an algebra which
resembles a ring of differential operators, but which is supposed to contain
information about a certain symplectic singularity associated to W.
Ginzburg, Guay, Opdam and Rouquier found a very nontrivial functor from a
category of modules over the Cherednik algebra to the category of
representations of the Hecke algebra. The aim of this talk is to show how
this functor can be used to prove things about the Hecke algebra in some
cases.