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Extended affine Weyl groups and Frobenius manifolds

Published online by Cambridge University Press:  04 December 2007

BORIS DUBROVIN  and
Youjin ZHANG
BORIS DUBROVIN
Affiliation:
SISSA, Via Beirut 2–4, 34014 Trieste, Italy, and Steklov Mathematics Institute, Moscow, e-mail: dubrovin@sissa.it
Youjin ZHANG
Affiliation:
SISSA, Via Beirut 2–4, 34014 Trieste, Italy, and Department of Mathematics, University of Science and Technology of China, Hefei, e-mail: youjin@sissa.it
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Abstract

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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 $F(t_1, …, t_n)$ of WDVV equations of associativity polynomial in $t_1, …, t_n-1$, exp $t_n$.

Keywords

root systemsaffine Weyl groupsFrobenius manifoldsflat coordinatesWDVV equations
Type
Research Article
Information
Compositio Mathematica , Volume 111 , Issue 2 , April 1998 , pp. 167 - 219
Copyright
© 1998 Kluwer Academic Publishers