Flat coordinates of Frobenius prepotentials related with the reflection groups of types $H_3$ and $H_4$

TL;DR

This paper explores the group-theoretic interpretation of flat coordinates in Frobenius prepotentials associated with reflection groups of types H_3 and H_4, building on previous algebraic constructions.

Contribution

It establishes a relation between flat coordinates of polynomial and algebraic prepotentials for H_3 and H_4 reflection groups using group-theoretic methods.

Findings

Derived a relation between flat coordinates of polynomial and algebraic prepotentials for H_3.

Extended the approach to H_4, connecting different prepotential types.

Provided a group-theoretic interpretation of these relations.

Abstract

In this article, we first explain a group theoretic interpretation of the derivation of the relation between the flat coordinates of the polynomial prepotential $(H_3)$ and those of the algebraic prepotential $(H_3)'$ given in \cite{KMS2} constructed by M. Feigin, D. Valeri and J. Wright \cite{FVW}. By the same idea explained in the case of $(H_3)$, we will show a relation between the flat coordinates of the polynomial prepotential $(H_4)$ and those of the algebraic prepotential $H_4(9)$ given in \cite{Se}.