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The Hodge filtration and the contact-order filtration of derivations of Coxeter arrangements. (English) Zbl 1082.32020

Summary: The Hodge filtration of the module of derivations on the orbit space of a finite real reflection group acting on an \(\ell\)-dimensional Euclidean space was introduced and studied by K. Saito [Publ. Res. Inst. Math. Sci. 29, No. 4, 535–579 (1993; Zbl 0828.15002) and ‘Finite reflection groups and related geometry’ (preprint 2000)]. It is closely related to the flat structure or the Frobenius manifold structure. We 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.

MSC:

32S22 Relations with arrangements of hyperplanes
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds

Citations:

Zbl 0828.15002
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References:

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