Extended affine Weyl groups and Frobenius manifolds

1998/04/01 by BORIS DUBROVIN, Boris Dubrovin, Youjin Zhang +1 · 11 citations
Mathematics · Chemistry · #Advanced Algebra and Geometry #Molecular spectroscopy and chirality #Axial and Atropisomeric Chirality Synthesis

paper · pdf · doi:10.1023/a:1000258122329

Abstract

We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley Theorem for their invariants, and construct a Frobenius structure on their orbit spaces. This produces solutions F(t₁, …, t_n) of WDVV equations of associativity polynomial in t₁, …, t_n-1 , exp t_n .

Cited by

• Open Hurwitz Flat F manifolds
• Dubrovin duality for open Hurwitz flat F-manifolds
• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• From primitive form to mirror symmetry
• Asymmetric rational reductions of 2D-Toda hierarchy and a generalized Frobenius manifold
• Frobenius manifold for the nodal quiver
• On enumeration of l-hypermaps
• The differential geometry of the orbit space of extended affine Jacobi group A
• Geometry and analytic theory of Frobenius manifolds
• A Frobenius manifold for ℓ-Kronecker quiver
• Finite orbits of the braid group action on sets of reflections

Related

• Extended affine Weyl groups and Frobenius manifolds -- II
• Extended V-systems and almost-duality for extended affine Weyl orbit spaces
• Generalized Frobenius Manifold Structures on the Orbit Spaces of Affine Weyl Groups I
• Differential Geometry of Orbit space of Extended Affine Jacobi Group A_n
• Geometry and analytic theory of Frobenius manifolds