Let $(W,S)$ be a Coxeter system and suppose that $w \in W$ is fullycommutative (in the sense of Stembridge) and has a reduced expression beginning(respectively, ending) with $s \in S$. If there exists $t\in S$ such that $s$and $t$ do not commute and $tw$ (respectively, $wt$) is no longer fullycommutative, we say that $w$ is left (respectively, right) weak star reducibleby $s$ with respect to $t$. In this paper, we classify the fully commutativeelements in Coxeter groups of types $B$ and affine $C$ that are irreducibleunder weak star reductions. In a sequel to this paper, the classification ofthe weak star irreducible elements in a Coxeter system of type affine $C$ willprovide the groundwork for inductive arguments used to prove the faithfulnessof a generalized Temperley--Lieb algebra of type affine $C$ by a particulardiagram algebra.
展开▼
机译：假设$（W，S）$为Coxeter系统，并假设W $中的$ w \是完全可交换的（就Stembridge而言），并且以S $中的$ s \开头（分别是结束）具有简化的表达式。如果在S $中存在$ t \，使得$ s $和$ t $不通勤，并且$ tw $（分别为$ wt $）不再完全可交换，我们说$ w $被保留（分别为右）相对于$ t $，可减少$ s $的弱恒星。在本文中，我们将Coxeter类型的$ B $和仿射$ C $的完全交换元素分类，这些元素在弱恒星减少下是不可约的。在本文的续篇中，在仿射$ C $型Coxeter系统中弱恒星不可约元素的分类将为归纳论证提供基础，该归纳论证用于证明a仿射$ C $型广义Temperley-Lieb代数的信度。 specialdiagram代数。
展开▼
