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The Hodge filtration and the contact-order filtration of derivations of Coxeter arrangements

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Abstract

The Hodge filtration of the module of derivations on the orbit space of a finite real reflection group acting on an ℓ-dimensional Euclidean space was introduced and studied by K. Saito [5] [6]. It is closely related to the flat structure or the Frobenius manifold structure. We will show that the Hodge filtration coincides with the filtration by the order of contacts to the reflecting hyperplanes. Moreover, a standard basis for the Hodge filtration is explicitly given.

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Authors and Affiliations

  1. Mathematics Department, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo, 192-0397, Japan

    Hiroaki Terao

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  1. Hiroaki Terao
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Correspondence to Hiroaki Terao.

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Partially supported by the Grant-in-aid for scientific research (No. 14340018 and 13874005), the Ministry of Education, Sports, Science and Technology, Japan

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Terao, H. The Hodge filtration and the contact-order filtration of derivations of Coxeter arrangements. manuscripta math. 118, 1–9 (2005). https://doi.org/10.1007/s00229-004-0536-z

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