Strangely dual orbifold equivalence I

TL;DR

This paper proves orbifold equivalence between two dual exceptional unimodular singularities, using matrix factorizations and analyzing Galois group actions to reveal deep symmetries in their algebraic structures.

Contribution

It establishes orbifold equivalence for specific singularities through novel matrix factorizations and Galois group analysis, providing new insights into their duality and symmetry.

Findings

Orbifold equivalence between $K_{14}$ and $Q_{10}$ singularities.

Matrix factorizations reveal solutions permuted by Galois groups.

Different expressions of the same singularity have distinct Galois group actions.

Abstract

In this brief note we prove orbifold equivalence between two potentials described by strangely dual exceptional unimodular singularities of type $K_{14}$ and $Q_{10}$ in two different ways. The matrix factorizations proving the orbifold equivalence give rise to equations whose solutions are permuted by Galois groups which differ for different expressions of the same singularity.