Susumu Ariki : Simple modules of the affine Hecke algebra of type A over $\mathbb C$

There are two constructions of simple modules of the affine Hecke algebra, one by the geometric method developed by Ginzburg, the other by combinatorial method developed by Dipper, James and Mathas (and the speaker). We show that crystal isomorphisms describe the module correspondence between the two constructions. Main tool is the modular branching rule for the affine Hecke algebra, which is established in this work. This is a joint work with Nicolas Jacon and Cedric Lecouvey.