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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1809.05026 |
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| _version_ | 1866917722357497856 |
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| author | Abe, Takuro Röhrle, Gerhard Stump, Christian Yoshinaga, Masahiko |
| author_facet | Abe, Takuro Röhrle, Gerhard Stump, Christian Yoshinaga, Masahiko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_05026 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups Abe, Takuro Röhrle, Gerhard Stump, Christian Yoshinaga, Masahiko Differential Geometry Combinatorics Group Theory 20F55, 52C35, 32S25 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. |
| title | A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups |
| topic | Differential Geometry Combinatorics Group Theory 20F55, 52C35, 32S25 |
| url | https://arxiv.org/abs/1809.05026 |