A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups
Differential Geometry
2024-07-17 v2 Combinatorics
Group Theory
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.
Keywords
Cite
@article{arxiv.1809.05026,
title = {A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups},
author = {Takuro Abe and Gerhard Röhrle and Christian Stump and Masahiko Yoshinaga},
journal= {arXiv preprint arXiv:1809.05026},
year = {2024}
}
Comments
20 pages, v2: minor corrections. Final version, to appear in J. Comb. Algebra