A reduction theorem for good basic invariants of finite complex reflection groups

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 d₁ of a finite complex reflection group G is regular and if is a divisor of d₁, a set of good basic invariants of G induces that of the reflection subquotient G_. 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_. Several examples of this reduction process are also presented.