AI 中文总结
研究B型wonderful模型上超八面体群作用的等变庞加莱多项式，通过等变关联代数反演公式将其化为A型级数与B型特征级数，并建立B型复合恒等式及显式公式。
AI 中文摘要
我们研究了超八面体群在由B型反射排列所关联的极小De Concini-Procesi wonderful模型的上同调上的作用。我们将它们的等变庞加莱多项式的生成级数表示为相应的A型级数与B型等变约化特征级数的函数。关键工具是等变关联代数中的一个一般反演公式，它将等变Chow函数与超约化特征函数联系起来。将该公式应用于划分格和符号划分格，我们恢复了Getzler在A型中的复合恒等式，并建立了其在B型中的类比。我们还获得了B型等变特征级数的显式plethystic和无限积公式。
英文摘要
We study the actions of hyperoctahedral groups on the cohomology of the minimal De Concini-Procesi wonderful models associated with reflection arrangements of type $B$. We express the generating series of their equivariant Poincaré polynomials in terms of the corresponding type $A$ series and the equivariant reduced characteristic series of type $B$. The key ingredient is a general inversion formula in equivariant incidence algebras relating equivariant Chow functions and super-reduced characteristic functions. Applying this formula to partition and signed partition lattices, we recover Getzler's compositional identity in type $A$ and establish its type $B$ analogue. We also obtain explicit plethystic and infinite-product formulas for the equivariant characteristic series of type $B$.
Comments36 pages
