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

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 $(H_3{)}^{\prime }$ 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}.