A Class of Infinite-dimensional Frobenius Manifolds and Their Submanifolds

TL;DR

This paper constructs a new class of infinite-dimensional Frobenius manifolds related to meromorphic functions and explores their connection to integrable hierarchies and finite-dimensional submanifolds linked to Coxeter groups.

Contribution

It introduces a novel class of infinite-dimensional Frobenius manifolds and establishes their relation to extended dispersionless BKP hierarchies and Coxeter group submanifolds.

Findings

Frobenius manifolds constructed on pairs of meromorphic functions

Principal hierarchies extend the dispersionless two-component BKP hierarchy

Finite-dimensional Frobenius submanifolds correspond to Coxeter groups of types B and D

Abstract

We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion relation, the principal hierarchies associated to such Frobenius manifolds are found to be certain extensions of the dispersionless two-component BKP hierarchy. Moreover, we show that these infinite-dimensional Frobenius manifolds contain finite-dimensional Frobenius submanifolds as defined on the orbit space of Coxeter groups of types B and D.