A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups

2018/09/13 by Takuro Abe, Gerhard Röhrle, Abe, Takuro +5 · 1 citation
Mathematics · #20F55 #32S25 #52C35 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1809.05026

openalex publication_date 2018/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an irreducible well-generated complex reflection group, we construct an explicit basis for the module of vector fields with logarithmic poles along its reflection arrangement. This construction yields in particular a Hodge filtration of that module. Our approach is based on a detailed analysis of a flat connection applied to the primitive vector field. This generalizes and unifies analogous results for real reflection groups.

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