In this paper, we show that the orbit space of the domain by the elliptic Weyl group for an elliptic root system of codimension 1 has a structure of Frobenius manifold. We also give a characterization of this structure of the Frobenius manifold under suitable conditions.
"Frobenius manifolds for elliptic root systems." Osaka J. Math. 47 (1) 301 - 330, March 2010.