Frobenius like structure of a family of arrangements with parallelly transported hyperplanes

Master functions of arrangements of hyperplanes appear in the Bethe ansatz constructions of eigenvectors of Hamiltonians of quantum integrable systems and in constructions of multidimensional hypergeometric solutions of the KZ type equations.  The algebra of functions on the critical set of a master function is closely related to the algebra of Hamiltonians of the associated quantum integrable model.

In this talk I will consider a family of arrangements with parallelly transported hyperplanes.  I will describe a Frobenius like structure on the base of the family in terms of the algebra of functions on the critical set of the associated master function.