In this talk I will explain the classification of the blocks of the Ariki-Koike algebras, which are certain finite dimensional quotients of the affine Hecke algebra of the general linear group. The key idea of the proof is not to work with the Ariki-Koike algebras at all and, instead, to classify the blocks of the cyclotomic Schur algebras. These latter algebras have the "same" blocks as the Ariki-Koike algebras and they have the added advantage that they are quasi-hereditary algebras. As a consequence, we can use a cute new trick with the Jantzen sum formula to reduce the classification of the blocks of the cyclotomic Schur algebras (and the Ariki-Koike algebras) to a purely combinatorial problem.
This is joint work with Sinéad Lyle.