Good Basic Invariants and Frobenius Structures

TL;DR

This paper introduces good basic invariants for finite complex reflection groups and demonstrates their connection to flat invariants and Frobenius structures, providing a new perspective on the algebraic structure of these groups.

Contribution

It defines good basic invariants for complex reflection groups and links them to Frobenius structures and flat invariants, extending previous work on real reflection groups.

Findings

Good basic invariants are defined for finite complex reflection groups.

These invariants relate to flat invariants of real reflection groups.

Taylor coefficients of invariants give structure constants of Frobenius algebra.

Abstract

In this paper, we define a set of good basic invariants for a finite complex reflection group under certain conditions. We show that a set of good basic invariants for a finite real reflection group gives a set of the flat invariants obtained by Saito and the Taylor coefficients of these good basic invariants give the structure constants of the multiplication of the Frobenius structure obtained by Dubrovin.