论文标题
Gelfand $ W $ - 古典Weyl群
Gelfand $W$-graphs for classical Weyl groups
论文作者
论文摘要
代数的Gelfand模型是由直接不可约的子模块给出的模块，每个不可约模块的同构类别都准确地表示。我们为有限的Coxeter组介绍了一个完美模型的概念，该组是一组离散数据（涉及雨水和Vazirani的完美互动概念），该数据为相关的Iwahori-Hecke代数参数参数为Gelfand模型。我们描述了所有古典Weyl群体的理想模型，不包括D型D型。这些模型附加的表示形式同时概括了Adin，Postnikov和Roichman（从A型到其他经典类型）以及Araujo和Bratten（从代数到Iwahori-Hecke代数）的构造。我们表明，从完美模型中得出的每个Gelfand模型都有一个规范的基础，从而产生了一对相关的$ W $ graphs，我们称之为Gelfand $ W $ -Graphs。对于BC和D类型，我们证明了这些$ W $绘图是彼此双重双重的，这种现象在A类型A中不出现。
A Gelfand model for an algebra is a module given by a direct sum of irreducible submodules, with every isomorphism class of irreducible modules represented exactly once. We introduce the notion of a perfect model for a finite Coxeter group, which is a certain set of discrete data (involving Rains and Vazirani's concept of a perfect involution) that parametrizes a Gelfand model for the associated Iwahori-Hecke algebra. We describe perfect models for all classical Weyl groups, excluding type D in even rank. The representations attached to these models simultaneously generalize constructions of Adin, Postnikov, and Roichman (from type A to other classical types) and of Araujo and Bratten (from group algebras to Iwahori-Hecke algebras). We show that each Gelfand model derived from a perfect model has a canonical basis that gives rise to a pair of related $W$-graphs, which we call Gelfand $W$-graphs. For types BC and D, we prove that these $W$-graphs are dual to each other, a phenomenon which does not occur in type A.
