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

2023/09/16 by Alexey Basalaev, Basalaev, Alexey · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2309.09054

openalex publication_date 2023/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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