Almost duality for Saito structure and complex reflection groups

TL;DR

This paper explores the reformulation of Dubrovin's almost duality for Frobenius structures into Saito structures without metric and investigates the existence and uniqueness of natural Saito structures on orbit spaces of complex reflection groups, providing complete results for irreducible groups.

Contribution

It introduces a new formulation of almost duality for Saito structures without metric and solves the existence and uniqueness problem for irreducible complex reflection groups.

Findings

Complete answer for irreducible groups

Reformulation of duality without metric

Insights into orbit space structures

Abstract

We reformulate Dubrovin's almost duality of Frobenius structures to Saito structures without metric. Then we formulate and study the existence and uniqueness problem of the natural Saito structure on the orbit spaces of finite complex reflection groups from the viewpoint of the almost duality. We give a complete answer to the problem for the irreducible groups.