Multipartitions, Generalized Durfee Squares and Affine Lie Algebra Characters

Standard multipartitions and a combinatorial affine Schur-Weyl duality

We introduce the notion of standard 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 complet…

Kleshchev 多重划分、仿射 Mirković-Vilonen 多面体以及 ${\tt A}^{(1)}_1$ 型 KLR 代数的表示

Kleshchev multipartitions, affine Mirković-Vilonen polytopes, and representations of KLR algebras in type ${\tt A}^{(1)}_1$

本文在 ${\tt A}_1^{(1)}$ 型 $B(\infty)$ 晶体的三个模型（仿射 MV 多面体、Kleshchev 多重划分和上缘图）之间构造显式同构，并给出直接完成仿射 MV 多面体和非迭代识别 Kleshchev 多重划分的结果，应用于 KLR 代数的表示理论。

Parameterizing Hecke algebra modules: Bernstein-Zelevinsky multisegments, Kleshchev multipartitions, and crystal graphs

This paper provides a combinatorial dictionary between three sets of objects: Bernstein-Zelevinsky multisegments, Kleshchev multipartitions, and the irreducible modules of the affine Hecke algebra $H_n$ (for generic $q$). In particular, we compute the action of the crystal operator $\tilde{e}_i$ (a refinement of socle of Restriction) on an irreducible module both in terms of its parameterization by multisegments and by multipartitions. In other words, we give explicit crystal graph isomorphisms. A byproduct is the determination of which multisegments parameterize modules of the {\it cyclotomic…

Two maps on affine type A crystals and Hecke algebras

We use the crystal isomorphisms of the Fock space to describe two maps on partitions and multipartitions which naturally appear in the crystal basis theory for quantum groups in affine type A and in the representation theory of Hecke algebras of type G(l, l, n).

仿射 A 型晶体中的面与典范基元素的形状

Faces in Crystals of Affine Type A and the Shape of Canonical Basis Elements

本文研究仿射 A 型晶体中的面结构，证明其保持缺陷的自同构，并构造长度为 2 的面内 $e$-正则多分拆及计数公式，进而给出典范基元素形状的闭式表达。

Core blocks of Ariki-Koike algebras II: the weight of a core block

We study combinatorial blocks of multipartitions, exploring further the notions of weight, hub and core block introduced by the author in earlier papers. We answer the question of which pairs (w,theta) occur as the weight and hub of a block, and we examine the action of the affine Weyl group on the set of blocks.