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 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 associated to gl_n. We show, in particular, the notion of standard multipartitions gives rise to a combinatorial deseription of the affine Sehur- Weyl duality in terms of a column-reading vs. row-reading of residues of a multipartition. This is based on a joint work with Jie Du.