论文标题
白人代表的B型类似物
A Type B analog of the Whitehouse representation
论文作者
论文摘要
我们通过引入$ b_ {n} $的家族来给出欧拉（Whitehouse）欧拉（Eulerian）表示从$ s_n $到$ s_ {n+1} $的type $ b $类似物。就像在类型$ a $中一样，我们通过在mantaci-reutenauer代数中的正交iDempotents进行组合解释这些表示形式，并拓扑为特定$ \ mathbb {z} _ {2} $ - orbit-orbit-orbit-orbit-orbit-orbit构造空间的共同体的分级片段。我们表明，提起的$ b_ {n+1} $ - 代表也具有配置空间的解释，并通过提供许多著名属性的模拟，例如与Equivariant共同体的连接和Varchenko-Gelfand Ring，进一步与类型$ a $ story平行。
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.
