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Main Authors: Konishi, Yukiko, Minabe, Satoshi
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2409.00380
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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