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

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

2009-10-14

arxiv.org/abs/0910.2506v1

Journal of Algebra, 330 (2011), 251-262

Mathematics

Combinatorics

Scientific paper

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.

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