仿射A型中的Kashiwara和Zelevinsky对合
Kashiwara and Zelevinsky involutions in affine type A
摘要：
我们首先描述如何柏原对合晶体的仿射型$A$编码的非周期性multisegments的组合。这产生了一个简单的关系，这个对合和Zelevinsky对合的集合上的简单模块的仿射Hecke代数。然后，我们给出了计算这些对合的有效程序。值得注意的是，这些过程并不使用底层的晶体结构。他们还允许明确匹配的金斯堡和Ariki参数化的简单模块相关的仿射和分圆Hecke代数，分别。
英文摘要：
We first describe how the Kashiwara involution on crystals of affine type $A$ is encoded by the combinatorics of aperiodic multisegments. This yields a simple relation between this involution and the Zelevinsky involution on the set of simple modules for the affine Hecke algebras. We then give efficient procedures for computing these involutions. Remarkably, these procedures do not use the underlying crystal structure. They also permit to match explicitly the Ginzburg and Ariki parametrizations of the simple modules associated to affine and cyclotomic Hecke algebras, respectively .
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