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

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.

56 pages. This is the newest version of arXiv:math/0502365 (23pages) Accepted by Advances in Mathematics (2019.5.20)

References in corpus (3)

• The Extended Bigraded Toda hierarchy
• Gromov--Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda Hierarchies
• Extended affine Weyl groups and Frobenius manifolds -- II

Cited by in corpus (16)

• Frobenius manifolds and a new class of extended affine Weyl groups ${\tilde{W}}^{(k,k+1)}(A_l)$
• Frobenius manifolds on orbits spaces
• Mirror symmetry for extended affine Weyl groups
• $E_8$ spectral curves
• The Differential Geometry of the Orbit Space of Extended Affine Jacobi Group $A_1$
• Trigonometric $\vee$-systems and solutions of WDVV equations
• Extended V-systems and almost-duality for extended affine Weyl orbit spaces
• Second-order integrable Lagrangians and WDVV equations
• Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality
• Solutions of $B{C}_n$ Type of WDVV Equations
• The Saito determinant for Coxeter discriminant strata
• The extended D-Toda hierarchy
• Dubrovin duality and mirror symmetry for ADE resolutions
• Diagonal invariants and genus-zero Hurwitz Frobenius manifolds
• Infinite-dimensional Frobenius Manifolds Underlying the Universal Whitham Hierarchy
• A Frobenius manifold for $\ell$-Kronecker quiver