## Abstract

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.

Original language | English |
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Article number | 107102 |

Journal | Journal of Pure and Applied Algebra |

Volume | 226 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 2022 |

## Keywords

- Affine Hecke algebra
- Affine Schur-Weyl duality
- Ariki-Koike algebra
- Drinfeld polynomial
- Quantum loop algebra
- Standard multipartition