Frobenius manifolds for elliptic root systems

TL;DR

This paper demonstrates that the quotient space of a domain by the reflection group of an elliptic root system forms a Frobenius manifold in codimension 1 and characterizes this structure under certain conditions.

Contribution

It establishes the Frobenius manifold structure on quotient spaces for elliptic root systems and provides a characterization under specific conditions.

Findings

Frobenius manifold structure exists for quotient spaces of elliptic root systems in codimension 1

A characterization of this Frobenius structure is provided under certain conditions

The structure relates to reflection groups and elliptic root systems

Abstract

In this paper, we show that the quotient space of the domain by the reflection group for an elliptic root system has a structure of Frobenius manifold for the case of codimension 1. We also give a characterization of this Frobenius manifold structure under some suitable condition.