Extended affine Weyl groups and Frobenius manifolds
Abstract
Description
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 $t_1, ..., t_{n-1}, \exp t_n$.
69 pages, amslatex, some references added, position of Table 1 is corrected. Revised version for Compositio Mathematica
69 pages, amslatex, some references added, position of Table 1 is corrected. Revised version for Compositio Mathematica