Geometry and Integrability in Mathematical Physics GIMP'06

May 15 - 19, 2006, Moscow, Russia

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Misha Feigin

Glascow University, UK

Logarithmic Frobenius structures and Coxeter discriminants

We consider a class of logarithmic solutions of the WDVV equations related to the special systems of covectors (V-systems). We show that the class is closed under taking subsystems and under restrictions to the intersections of the corresponding hyperplanes. Starting from the Coxeter systems the restriction procedure leads to the multiplication structures which are dual in Dubrovin's sense to the Frobenius structures on the Coxeter discriminants discussed by Strachan. On this way we recover known families of V-systems and also obtain new V-systems. This is a joint work with A.P.Veselov.