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Extended affine Weyl groups and Frobenius manifolds

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Compositio Mathematica

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

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Authors and Affiliations

  1. SISSA, Via Beirut 2–4, 34014, Trieste, Italy

    Boris Dubrovin & Youjin Zhang

  2. Steklov Mathematics Institute, Moscow

    Boris Dubrovin

  3. Department of Mathematics, University of Science and Technology of China, Hefei

    Youjin Zhang

Authors
  1. Boris Dubrovin
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  2. Youjin Zhang
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Dubrovin, B., Zhang, Y. Extended affine Weyl groups and Frobenius manifolds. Compositio Mathematica 111, 167–219 (1998). https://doi.org/10.1023/A:1000258122329

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