怀特豪斯表示法的B型模拟
A Type B analog of the Whitehouse representation
摘要：
通过引入一族提升到$B_{n+1}$的$B_{n}$ -表示，我们给出了Whitehouse将欧拉表示从$S_n$提升到$S_{n+1}$的$B$型模拟.在$A$型中，我们通过Mantaci-Schottenauer代数中的正交幂等元族组合地解释这些表示，并在拓扑上解释为$\mathbb{R}^{3}$的某个$\mathbb{Z}_{2}$ -轨道位形空间的上同调的分次片段。我们发现，解除$B_{n+1}$ -表示也有一个配置空间的解释，并进一步平行的$A$型故事，它的许多显着的属性，如连接到等变上同调和Varchenko-Gelfand环。
英文摘要：
We give a Type $B$ analog of Whitehouse's lifts of the Eulerian representations from $S_n$ to $S_{n+1}$ by introducing a family of $B_{n}$-representations that lift to $B_{n+1}$. As in Type $A$, we interpret these representations combinatorially via a family of orthogonal idempotents in the Mantaci-Reutenauer algebra, and topologically as the graded pieces of the cohomology of a certain $\mathbb{Z}_{2}$-orbit configuration space of $\mathbb{R}^{3}$. We show that the lifted $B_{n+1}$-representations also have a configuration space interpretation, and further parallel the Type $A$ story by giving analogs of many of its notable properties, such as connections to equivariant cohomology and the Varchenko-Gelfand ring.
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