Standard multipartitions and a combinatorial affine Schur-Weyl duality

We introduce the notion of standard (Kleshchev) multipartitions and establish a one-to-one correspondence between standard multipartitions and irreducible representations with integral weights for the affine Hecke algebra of type A with a parameter q∈C^× which is not a root of unity. We then extend the correspondence to all Kleshchev multipartitions for Ariki-Koike algebras of integral type. By the affine Schur–Weyl duality, we further extend this to a correspondence between standard multipartitions and Drinfeld multipolynomials of integral type whose associated irreducible polynomial representations completely determine all irreducible polynomial representations for the quantum loop algebra U_q(glˆ_n). We will see, in particular, the notion of standard multipartitions gives rise to a combinatorial description of the affine Schur–Weyl duality in terms of a column-reading vs. row-reading of residues of a multipartition.