Hecke代数和Coxeter群表示的箭图数据
Quiver data of representations of Hecke algebras and Coxeter groups
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中文总结 AI 辅助
研究Hecke代数和Coxeter群表示的箭图数据，提出[Γ;q]型H-表示概念，通过其与Hq(Γ)-表示的关系构造非相交表示，还引入H²-表示，开发构造程序并证明特定条件下H²-表示的可实现性。
中文摘要 AI 辅助
设Γ为Coxeter矩阵，q为一般参数，Hq(Γ)为岩堀-赫克代数。我们提出了[Γ;q]型H-表示的概念，它是满足若干组关系的特定箭图的表示。我们表明[Γ;q]型H-表示与Hq(Γ)-表示几乎相互确定。利用此构造所有不相交的Hq(Γ)-表示。H-表示与Kazhdan-Lusztig理论兼容。提出了H-表示与W-图之间的一些关系，为W-图给出Hq(Γ)的W-表示生成一个方程组。为构造一般型Hq(Γ)-表示，引入了H²-表示概念。开发了从选定的[Γ;q]可实现的H²-表示构造一般型H-表示的程序，证明若Γ满足对任意i≠j有m_(i,j)≥5，则任何H²-表示都是[Γ;q]可实现的。
英文摘要
Let Gamma be a Coxeter matrix and q be a generic parameter, let Hq (Gamma) be the Iwahori-Hecke algebra. We propose a concept H-representation of type [Gamma;q], which are representations of certain quiver satisfying several sets of relations. We show type [Gamma;q] H-representation and Hq (Gamma)-representation almost determine each other. By using this we construct all nonintersecting type Hq (Gamma)-representations . H-representation is compatible with the Kazhdan-Lusztig theory . Some relations between H-representation and W-graph are proposed, which produce an equation system for a W-graph to giving a W-representation of Hq (Gamma) . With the intention of constructing general type Hq (Gamma)-representations we introduce the concept H^2 -representation , which is another quiver representation hidden in a H-representation. A program to construct general type H-representations from a chosen [Gamma;q]-realizable H^2 -representation is developed ,by using it we prove that if Gamma satisfies m_(i,j) >= 5 for any i not equal to j, then any H^2 -representation is [ Gamma;q]-realizable.
