Mathematische Zeitschrift

, Volume 264, Issue 4, pp 813–828 | Cite as

A primitive derivation and logarithmic differential forms of Coxeter arrangements



Let W 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.


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© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsKyoto UniversityKyotoJapan
  2. 2.Department of MathematicsHokkaido UniversitySapporo, HokkaidoJapan

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