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

We define primitive derivations for Coxeter arrangements which may not be irreducible. Using those derivations, we introduce the 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 was studied in Abe and Terao (2010) [2], which generalizes the Hodge filtration introduced by K. Saito (e.g., Saito, 2003 [6]).