A generalized logarithmic module and duality of Coxeter multiarrangements

Coxeter multiarrangements with quasi-constant multiplicities

We study structures of derivation modules of Coxeter multiarrangements with quasi-constant multiplicities by using the primitive derivation. As an application, we show that the characteristic polynomial of a Coxeter multiarrangement with quasi-constant multiplicity is combinatorially computable.

多超平面排列上对数形式的删除-限制

Deletion-Restriction for Logarithmic Forms on Multiarrangements

研究超平面排列与多排列中对数微分形式在删除和限制操作下的行为，通过交换代数度量满射性缺失，并证明自由排列添加超平面后具有“对偶强加一生成”性质。

多重排列的导子的积分表达式

Integral expressions for derivations of multiarrangements

本文受量子Calogero-Moser系统拟不变量积分表达式的启发，为若干自由多重排列构造了特定基的积分表达式，并推广到二维三直线及复反射群相关情形，还对类型B_2扩展Catalan排列的对数向量场模提出猜想性基。

Primitive filtrations of the modules of invariant logarithmic forms of Coxeter arrangements

We define {\bf primitive derivations} for Coxeter arrangements which may not be irreducible. Using those derivations, we introduce the {\bf primitive filtrations} of the module of invariant logarithmic differential forms for an arbitrary Coxeter arrangement with an arbitrary multiplicity. In particular, when the Coxeter arrangement is irreducible with a constant multiplicity, the primitive filtration has already been studied, which generalizes the Hodge filtration introduced by K. Saito.