Frobenius manifolds and a new class of extended affine Weyl groups of BCD-type

Abstract

Let R be an irreducible reduced root system, we firstly construct a flat pencil of metrics on the orbit space Mk,k+r(R)∖Σr of the extended affine Weyl group W˜(k,k+r)(R) for 1≤k<k+r≤l, where R=Bl,Cl,Dl. Afterwards, we construct a class of Frobenius manifold structures on the space consisting of particular cosine-Laurent series. Finally we show that for a given integer 0≤m≤l−k−r, there is a unique Frobenius manifold structure of charge 1 on the orbit space Mk,k+r(R)∖Σr of W˜(k,k+r)(R) satisfying certain conditions.