论文标题
原始派生和离散积分
The Primitive Derivation and Discrete Integrals
论文作者
论文摘要
已知与根系相关的（扩展）加泰罗尼亚和SHI排列的对数衍生物的模块已知是免费的。但是，除少数情况外，此类模块的明确基础尚不清楚。在本文中，我们为$ a $ root Systems构建明确的基础。我们的构建基于Bandlow-Musiker的积分公式，用于Quasiinvariants空间的基础。积分公式可以被视为K. saito引入的原始衍生物倒数的表达式。我们证明，整体公式的离散类似物为加泰罗尼亚和SHI布置提供了基础。
The modules of logarithmic derivations for the (extended) Catalan and Shi arrangements associated with root systems are known to be free. However, except for a few cases, explicit bases for such modules are not known. In this paper, we construct explicit bases for type $A$ root systems. Our construction is based on Bandlow-Musiker's integral formula for a basis of the space of quasiinvariants. The integral formula can be considered as an expression for the inverse of the primitive derivation introduced by K. Saito. We prove that the discrete analogues of the integral formulas provide bases for Catalan and Shi arrangements.
