A reduction theorem for good basic invariants of finite complex reflection groups
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909573033492480 |
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| author | Konishi, Yukiko Minabe, Satoshi |
| author_facet | Konishi, Yukiko Minabe, Satoshi |
| contents | This is a sequel to our previous article arXiv:2307.07897. We describe a certain reduction process of Satake's good basic invariants. We show that if the largest degree $d_1$ of a finite complex reflection group $G$ is regular and if $δ$ is a divisor of $d_1$, a set of good basic invariants of $G$ induces that of the reflection subquotient $G_δ$. We also show that the potential vector field of a duality group $G$, which gives the multiplication constants of the natural Saito structure on the orbit space, induces that of $G_δ$. Several examples of this reduction process are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00380 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A reduction theorem for good basic invariants of finite complex reflection groups Konishi, Yukiko Minabe, Satoshi Algebraic Geometry Mathematical Physics Primary 53D45, Secondary 20F55 This is a sequel to our previous article arXiv:2307.07897. We describe a certain reduction process of Satake's good basic invariants. We show that if the largest degree $d_1$ of a finite complex reflection group $G$ is regular and if $δ$ is a divisor of $d_1$, a set of good basic invariants of $G$ induces that of the reflection subquotient $G_δ$. We also show that the potential vector field of a duality group $G$, which gives the multiplication constants of the natural Saito structure on the orbit space, induces that of $G_δ$. Several examples of this reduction process are also presented. |
| title | A reduction theorem for good basic invariants of finite complex reflection groups |
| topic | Algebraic Geometry Mathematical Physics Primary 53D45, Secondary 20F55 |
| url | https://arxiv.org/abs/2409.00380 |