Generators of the Hecke algebra of (S(2n), B(n))

Let K=B(n) denote the hyperoctahedral subgroup of the symmetric group G=S(2n).
In this talk, building on an old work of Farahat and Higman on the centers of the group rings of symmetric groups,
we construct a set of ring generators for the (Hecke) algebra of bi-K-invariant functions on G.
If time permits we will talk about various consequences of our work, including a description of the total cohomology ring of the Hilbert scheme of n-points in the plane.

This is a joint work with Kursat Aker from Middle East Technical University, Turkey.