论文标题
反射安排补充的共同体中不变和半不变的
Invariants and semi-invariants in the cohomology of the complement of a reflection arrangement
论文作者
论文摘要
假设V是一个有限的尺寸，复杂的矢量空间，A是V的有限的CODIMINES一个子空间，G是通用线性GL（V）的有限亚组，它在A中排列了A的超平面。在本文中，我们研究了不变性和半融合的QG模型H^*（m（m），其中A（a）的A My（A） H^*（。）表示理性的奇异共同体，在A为反射布置的情况下，这对（a，g）来自反射套件。我们的主要结果是建造不变空间的显式，自然的（从Coxeter组的角度来看），H^*（m（a））^g。除了证明不依赖计算机计算的Coxeter组猜想的不变空间的描述外，此构建提供了对不变空间的这种描述，以扩展到任意有限的，复杂的反射组。主要结果还导致简化了Lehrer，Callegaro-Marin和Marin的一些共同学计算。
Suppose V is a finite dimensional, complex vector space, A is a finite set of codimension one subspaces of V, and G is a finite subgroup of the general linear group GL(V) that permutes the hyperplanes in A. In this paper we study invariants and semi-invariants in the graded QG-module H^*(M(A)), where M(A) denotes the complement in V of the hyperplanes in A and H^*( . ) denotes rational singular cohomology, in the case when A is a reflection arrangement and the pair (A,G) arises from a reflection coset. Our main result is the construction of an explicit, natural (from the point of view of Coxeter groups) basis of the space of invariants, H^*(M(A))^G. In addition to leading to a proof of the description of the space of invariants conjectured by Felder and Veselov for Coxeter groups that does not rely on computer calculations, this construction provides an extension of this description of the space of invariants to arbitrary finite, complex reflection groups. The main result also leads to simplifications of some cohomology computations of Lehrer, Callegaro-Marin, and Marin.
