关于$\tilde C$型的全交换元素及相关塔的忠实性
On the fully commutative elements of type $\tilde C$ and faithfulness of related towers
摘要：
我们为$n\geq 1$定义了一个$\tilde{C}$型Coxeter群$W(\tilde C_{n})$的注入塔.我们定义了一个Hecke代数的塔，我们使用在Coxeter水平上的忠实性来证明这最后一个塔是一个注入塔。设$W^c(\tilde C_{n})$是$W(\tilde C_{n})$中完全可交换元素的集合，我们对$W^c(\tilde C_{n})$的元素进行了分类并给出了它们的范式。我们使用该范式定义从$W^c(\tilde C_{n-1})$到$W^c(\tilde C_{n})$的两个注入。然后我们定义了$\tilde{C }$型仿射Temperley-Lieb代数的塔，并使用上面的注入来证明这个塔的忠实性。
英文摘要：
We define a tower of injections of $\tilde{C}$-type Coxeter groups $W(\tilde C_{n})$ for $n\geq 1$. We define a tower of Hecke algebras and we use the faithfulness at the Coxeter level to show that this last tower is a tower of injections. Let $W^c(\tilde C_{n})$ be the set of fully commutative elements in $W(\tilde C_{n})$, we classify the elements of $W^c(\tilde C_{n})$ and give a normal form for them. We use this normal form to define two injections from $W^c(\tilde C_{n-1})$ into $W^c(\tilde C_{n})$. We then define the tower of affine Temperley-Lieb algebras of type $\tilde{C }$ and use the injections above to prove the faithfulness of this tower.
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