Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials

TL;DR

This paper extends the construction of Frobenius manifolds and Landau-Ginzburg superpotentials to orbit spaces of extended affine Weyl groups of types B, C, and D, generalizing previous results to all Dynkin diagram vertices.

Contribution

It introduces Frobenius manifold structures on these orbit spaces for all Dynkin diagram vertices, not just a specific case, and constructs corresponding LG superpotentials.

Findings

Frobenius structures exist for all vertices of the Dynkin diagrams

Construction of LG superpotentials for these structures

Generalization of previous results to broader cases

Abstract

For the root systems of type $B_l, C_l$ and $D_l$, we generalize the result of \cite{DZ1998} by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in \cite{DZ1998}. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures.