FJRW rings and Landau-Ginzburg Mirror Symmetry
Abstract
In this article, we study the Berglund--H\"ubsch transpose construction WT for invertible quasihomogeneous potential W. We introduce the dual group GT and establish the state space isomorphism between the Fan-Jarvis-Ruan-Witten A-model of W/G and the orbifold Milnor ring B-model of WT/GT. Furthermore, we prove a mirror symmetry theorem at the level of Frobenius algebra structure for Gmax. Then, we interpret Arnol'd strange duality of exceptional singularities W as mirror symmetry between W/J and its strange dual WSD.
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