论文标题
签名排列的HOPF代数的高核心体组的弱顺序和单一基础
The weak order on the hyperoctahedral group and the monomial basis for the Hopf algebra of signed permutations
论文作者
论文摘要
我们给出了高度二十体群的弱顺序的组合描述。然后，该表征用于分析高肠面积偏移产物的顺序理论特性。结果表明，每种移位的产品都是某些间隔的不相交联合，可以将其嵌入到高粒面体中。作为应用程序，我们研究了签名的排列的Hopf代数$ \ Mathfrak {H} sym $的单一基础，这与MöbiusiNversion在高核方面的弱顺序上相关。事实证明，从$ \ mathfrak {h} sym $到$ b $ b $ quasi-Metresmmetric函数的代数为零或单级准对称函数$ b $的代数为代数。
We give a combinatorial description for the weak order on the hyperoctahedral group. This characterization is then used to analyze the order-theoretic properties of the shifted products of hyperoctahedral groups. It is shown that each shifted product is a disjoint union of some intervals, which can be convex embedded into a hyperoctahedral group. As an application, we investigate the monomial basis for the Hopf algebra $\mathfrak{H}Sym$ of signed permutations, related to the fundamental basis via Möbius inversion on the weak order on hyperoctahedral groups. It turns out that the image of a monomial basis element under the descent map from $\mathfrak{H}Sym$ to the algebra of type $B$ quasi-symmetric functions is either zero or a monomial quasi-symmetric function of type $B$.
