Extended affine Weyl groups and Frobenius manifolds

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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, …, tn) of WDVV equations of associativity polynomial in t1, …, tn−1, exp tn.

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