论文标题
Aggine Hecke代数中的缠结
Tangles in affine Hecke algebras
论文作者
论文摘要
类型$ a $的Aggine Hecke代数$ \ dot h_n $通常以$ n $ braids的编织代数的商表示。这导致了环上的编织形式的示意图，但要对简单的Artin辫子的二次关系，如Graham和Lehrer在\ cite {Gl03}中的描述中。 我在这里表明，在Annulus中使用更通用的面向框架的$ n $ tangle图（受Homfly skein Ressption的约束）产生一个代数，该代数与$ \ dot h_n $同构具有带有系数的环形环。此设置允许使用一些有吸引力的图表，用于$ \ dot h_n $的元素，使用封闭曲线和编织物，并为其中心元素提供整洁的图片。
The affine Hecke algebra $\dot H_n$ of type $A$ is often presented as a quotient of the braid algebra of $n$-braids in the annulus. This leads to diagrammatic representations in terms of braids in the annulus, subject to a quadratic relation for the simple Artin braids, as in the description by Graham and Lehrer in \cite{GL03}. I show here that the use of more general framed oriented $n$-tangle diagrams in the annulus, subject to the Homfly skein relations, produces an algebra which is isomorphic to $\dot H_n$ with an extended ring of coefficients. This setting allows the use of some attractive diagrams for elements of $\dot H_n$, using closed curves as well as braids, and gives neat pictures for its central elements.
