Extended affine Weyl groups and Frobenius manifolds

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 $F(t_1,...,t_n)$ of WDVV equations of associativity polynomial in $t_1,...,t_{n-1},\exp t_n$.

arXiv comment69 pages, amslatex, some references added, position of Table 1 is corrected. Revised version for Compositio Mathematica

Cited by in corpus (7)

• Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials
• Weyl groups and Elliptic Solutions of the WDVV equations
• Additional symmetries of the extended bigraded Toda hierarchy
• Mirror symmetry for extended affine Weyl groups
• Five-dimensional gauge theories and the local B-model
• Darboux transformations and Fay identities for the extended bigraded Toda hierarchy
• A Class of Infinite-dimensional Frobenius Manifolds and Their Submanifolds