A primitive derivation and logarithmic differential forms of Coxeter arrangements
Combinatorics
2010-02-19 v3 Algebraic Geometry
Representation Theory
Abstract
Let be a finite irreducible real reflection group, which is a Coxeter group. We explicitly construct a basis for the module of differential 1-forms with logarithmic poles along the Coxeter arrangement by using a primitive derivation. As a consequence, we extend the Hodge filtration, indexed by nonnegative integers, into a filtration indexed by all integers. This filtration coincides with the filtration by the order of poles. The results are translated into the derivation case.
Keywords
Cite
@article{arxiv.0810.3107,
title = {A primitive derivation and logarithmic differential forms of Coxeter arrangements},
author = {Takuro Abe and Hiroaki Terao},
journal= {arXiv preprint arXiv:0810.3107},
year = {2010}
}