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Mirror map for Fermat polynomial with non-abelian group of symmetries (2103.16884v2)

Published 31 Mar 2021 in math.AG, math-ph, and math.MP

Abstract: We study Landau-Ginzburg orbifolds $(f,G)$ with $f=x_1n+\ldots+x_Nn$ and $G=S\ltimes Gd$, where $S\subseteq S_N$ and $Gd$ is either the maximal group of scalar symmetries of $f$ or the intersection of the maximal diagonal symmetries of $f$ with $\mathrm{SL}_N(\mathbb{C})$. 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 $n=N=5$.

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