论文标题
自旋链作为仿射temperley-lieb代数上的模块
Spin chains as modules over the affine Temperley-Lieb algebra
论文作者
论文摘要
Aggine temperley-lieb代数$ \ mathsf {a} \ hskip-1.8pt \ mathsf {tl} _ {n}（β）$是一个无限二维代数，该代数由数字$β\ in \ in \ mathbb {c} $ ninteger $ ninte $ n Integer and an and ande $ n \ n \ n \ n \ n \ in \ in \ in \ in \ in \ in \ in它自然作用于$（\ mathbb {c}^2）^{\ otimes n} $，以产生一个由附加参数$ z \ in \ mathbb c^\ times $的代表性家族。这些表示形式的结构是由Pasquier和Saleur在其旋转链的研究中首先引入的。他们与蜂窝$ \ Mathsf {a} \ hskip-1.8pt \ Mathsf {tl} _ {n}（β）$ - 格雷厄姆和勒勒的模块不同，但与后者表示的loeewy and arrows的方向有所不同。该陈述的证据使用了Morin-Duchesne和Saint-aubin引入的形态学以及新的地图，这些地图交织了各种$ \ Mathsf {a} \ hskip-1.8pp \ hskip-1.8pt \ shssf {tl} _ {tl} _ {n} _ {n}（β）（β）（β）（β）$ - 在xxz链上进行的twitchit $ and e e e e e e e e e e e y \ exteriation ^ Morin-Duchesne和Saint-Aubin。
The affine Temperley-Lieb algebra $\mathsf{a}\hskip-1.8pt\mathsf{TL}_{N}(β)$ is an infinite-dimensional algebra parametrized by a number $β\in \mathbb{C}$ and an integer $N\in \mathbb{N}$. It naturally acts on $(\mathbb{C}^2)^{\otimes N}$ to produce a family of representations labeled by an additional parameter $z\in\mathbb C^\times$. The structure of these representations, which were first introduced by Pasquier and Saleur in their study of spin chains, is here made explicit. They share their composition factors with the cellular $\mathsf{a}\hskip-1.8pt\mathsf{TL}_{N}(β)$-modules of Graham and Lehrer, but differ from the latter representations by the direction of about half of the arrows of their Loewy diagrams. The proof of this statement uses a morphism introduced by Morin-Duchesne and Saint-Aubin as well as new maps that intertwine various $\mathsf{a}\hskip-1.8pt\mathsf{TL}_{N}(β)$-actions on the XXZ chain and generalize applications studied by Deguchi $\textit{et al}$ and after by Morin-Duchesne and Saint-Aubin.
