Mirror map for Fermat polynomials with a nonabelian group of symmetries
We study Landau-Ginzburg orbifolds (f,G) with f=xn1+…+xnN and G=S⋉Gd, where S⊆SN and Gd is either the maximal group of scalar symmetries of f or the intersection of the maximal diagonal symmetries of f with SLN(ℂ). We construct a mirror map between the corresponding phase spaces and prove that it is an isomorphism restricted to a certain subspace of the phase space when n=N is a prime number. When S satisfies the condition PC of Ebeling and Gusein-Zade this subspace coincides with the full space. We also show that two phase spaces are isomorphic for n=N=5.