论文标题
仿射类型$ \ wideTilde {b} $和$ \ widetilde {d} $的广义temperley-lieb代数的图表表示
Diagrammatic representations of Generalized Temperley-Lieb algebras of affine type $\widetilde{B}$ and $\widetilde{D}$
论文作者
论文摘要
令$（w，s）$为类型$ \ wideTilde {b} $或$ \ widetilde {d} $和$ {\ rm tl}（w）$相应的广义temperley-lieb代数。在本文中，我们定义了由装饰图制成的无限尺寸关联代数，该代数是同构为$ {\ rm tl}（w）$。此外，我们描述了这样一个代数的明确依据，该代数由我们称为接受的特殊装饰图组成。这样的基础是与$ w $完全交换元素索引的广义temperley-lieb代数的经典单元基础的徒函数。
Let $(W,S)$ be an affine Coxeter system of type $\widetilde{B}$ or $\widetilde{D}$ and ${\rm TL}(W)$ the corresponding generalized Temperley-Lieb algebra. In this paper we define an infinite dimensional associative algebra made of decorated diagrams that is isomorphic to ${\rm TL}(W)$. Moreover, we describe an explicit basis for such an algebra consisting of special decorated diagrams that we call admissible. Such basis is in bijective correspondence with the classical monomial basis of the generalized Temperley-Lieb algebra indexed by the fully commutative elements of $W$.
