Frobenius manifolds and quantum groups

TL;DR

This paper establishes a connection between isomonodromy KZ connections and Frobenius manifolds, showing that classical limits of quantum structures recover known geometric frameworks in integrable systems.

Contribution

It introduces isomonodromy KZ connections related to quantum Stokes matrices and demonstrates their classical limit yields Frobenius and flat F-manifold structures.

Findings

Classical limit of quantum KZ connections corresponds to Dubrovin connections.

Quantum Stokes matrices are central to the isomonodromy KZ connections.

The work bridges quantum group theory and Frobenius manifold geometry.

Abstract

We introduce isomonodromy Knizhnik-Zamolodchikov (KZ) connections with respect to the quantum Stokes matrices, and prove that the classical limit of the KZ type connections gives rise to the Dubrovin connections of semisimple Frobenius manifolds and flat F-manifolds.