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We give an equivariant version of the Saito duality which can be regarded as a Fourier transformation on Burnside rings. We show that (appropriately defined) reduced equivariant monodromy zeta functions of Berglund–Hübsch dual invertible polynomials are Saito dual to each other with respect to their groups of diagonal symmetries. Moreover, we show that the relation between ‘geometric roots’ of the monodromy zeta functions for some pairs of Berglund–Hübsch dual invertible polynomials described in a previous paper is a particular case of this duality.

Saito duality between Burnside rings for invertible polynomials