Primitive filtrations of the modules of invariant logarithmic forms of Coxeter arrangements
arXiv:0910.2506 · doi:10.1016/j.jalgebra.2010.12.010
Abstract
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.