超平面的排列Ⅰ：有理函数与Jeffrey-Kirwan剩余
Arrangements of hyperplanes I: Rational functions and Jeffrey-Kirwan residue
摘要：
考虑空间$R_Δ$的有理函数的几个变量与极点上的一个固定的安排$Δ$的超平面。我们得到了常系数微分算子环上的模$R_Δ$的一个分解。我们推广到空间$R_Δ$的主部和剩余的概念，我们描述了它的关系，拉普拉斯变换的局部多项式函数。这解释了代数方面的工作L。Jeffreys和F.关于Hamilton流形上等变上同调类积分的Kirwan定理。作为另一个应用，我们将在后面的文章中构造多维形式的爱森斯坦级数，并得到A的一个留数公式的另一个证明。Szenes的Witten zeta函数。
英文摘要：
Consider the space $R_Δ$ of rational functions of several variables with poles on a fixed arrangement $Δ$ of hyperplanes. We obtain a decomposition of $R_Δ$ as a module over the ring of differential operators with constant coefficients. We generalize to the space $R_Δ$ the notions of principal part and of residue, and we describe its relations to Laplace transforms of locally polynomial functions. This explains algebraic aspects of work by L. Jeffreys and F. Kirwan about integrals of equivariant cohomology classes on Hamiltonian manifolds. As another application, we will construct multidimensional versions of Eisenstein series in a subsequent article, and we will obtain another proof of a residue formula of A. Szenes for Witten zeta functions.
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