FJRW rings and Landau-Ginzburg Mirror Symmetry

Understand

In this article, we study the Berglund--H\"ubsch transpose construction W^T for invertible quasihomogeneous potential W.

• We introduce the dual group G^T 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 W^T/G^T.
• Furthermore, we prove a mirror symmetry theorem at the level of Frobenius algebra structure for G^max.
• Then, we interpret Arnol'd strange duality of exceptional singularities W as mirror symmetry between W/J and its strange dual W^SD.