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In Gepner's pioneering work, the requirement that leads to a model having the desired N=1 Spacetime supersymmetry and E(8)×E(6) Gauge symmetry was the requirement that the spacetime symmetry is compatible with modular invariance. In this work we show that the requirement for the simultaneous fulfillment of mutual locality of the left-moving vertices of physical states with the space-time symmetry generators and of right-moving vertices with generators of E(8)×E(6)-gauge symmetry, which arises after some special reduction together with the requirement of mutual locality of complete (left-right) vertices of physical states among themselves leads to the same Gepner models.

We consider the CY orbifolds connected with the products of N=(2,2) supersymmetric minimal models. We use the spectral flow construction of states, as well as its mirror one, to explicitly show that these CY orbifolds are canonically combined into mirror pairs of isomorphic models, associated to the mutually dual pairs of admissible groups of Berglund-Hubsh-Krawitz.