A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups
Copyright policy )A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups
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.
- Osaka University Japan
- Ruhr University Bochum Germany
- Rikkyo University Japan
Mathematics - Differential Geometry, unitary reflection group, Group Theory (math.GR), Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Complex surface and hypersurface singularities, Reflection and Coxeter groups (group-theoretic aspects), Differential Geometry (math.DG), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 20F55, 52C35, 32S25, Mathematics - Group Theory, logarithmic vector field, Hodge filtration
Mathematics - Differential Geometry, unitary reflection group, Group Theory (math.GR), Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Complex surface and hypersurface singularities, Reflection and Coxeter groups (group-theoretic aspects), Differential Geometry (math.DG), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 20F55, 52C35, 32S25, Mathematics - Group Theory, logarithmic vector field, Hodge filtration
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