STRUCTURE OF SEMISIMPLE POLYNOMIAL FROBENIUS MANIFOLD

Abstract

Dubrovin conjectured that all polynomial semisimple Frobenius manifolds are equivalent to either the orbit space of Coxeter group C^(n)/W or their finite direct sum C^(n1)/W_(1) □ㆍㆍㆍ□C^(nk)/W_(k). In this paper, we investigate the monodromy data and monodromy group on direct sum of the orbit spaces of Coxeter groups. Using this, we give the proof of the conjecture depending only on monodromy group. Also we show that the induced G-function on the latter space is the sum of G-functions on each component up to constant.