ИСТИНА

Earlier there was defined an equivariant version of the so-called Saito duality between the monodromy zeta functions as a sort of Fourier transform between the Burnside rings of an abelian group and of its group of characters. We define a so-called enhanced Burnside ring of a finite group G. An element of it is represented by a finite G-set with a G-equivariant transformation and with characters of the isotropy subgroups associated to all points. We give an enhanced version of the equivariant Saito duality. For a complex analytic G-manifold with a G-equivariant transformation of it one has an enhanced equivariant Euler characteristic with values in a completion of theenhanced Burnside ring. Berglund-Hübsch-Henningson dual pairs consisting of so called invertible polynomials and abelian groups of their symmetries were defined in the framework of the Mirror symmetry. It is proved that the (reduced) enhanced equivariant Euler characteristics of the Milnor fibres of Berglund-Hübsch dual invertible polynomials coincide up to sign and show that this implies the result about the orbifold zeta functions of Berglund-Hübsch-Henningson dual pairs obtained earlier. The talk is based on a joint work with W. Ebeling.