On B type family of Dubrovin-Frobenius manifolds and their integrable systems

TL;DR

This paper explores the structure of B type Dubrovin-Frobenius manifolds linked to Coxeter groups, revealing relations between different indices and extending integrable hierarchies like the dispersionless BKP hierarchy.

Contribution

It uncovers relations between Dubrovin-Frobenius manifolds with different indices and extends the dispersionless BKP hierarchy through associated integrable PDEs.

Findings

Part of the data of (k,l) indexed manifolds can be recovered from (k+r,l+r) cases.

Established connections between different B type Frobenius manifolds.

Extended the dispersionless BKP hierarchy with new integrable PDEs.

Abstract

According to D.Zuo and an unpulished work of M.Bertola, there is a two--index series of Dubrovin--Frobenius manifold structures associated to a B type Coxeter group. We study the relations between these structures for the different values of these indices. We show that part of the data of such Dubrovin--Frobenius manifold indexed by $(k,l)$ can be recovered by the $(k+r,l+r)$ Dubrovin--Frobenius manifold. Continuing the program of arXiv:2007.11974 we associate an infinite system of commuting PDEs to these Dubrovin--Frobenius manifolds and show that these PDEs extend the dispersionless BKP hierarchy.