Abstract We study the bigraded vector space structure of Landau–Ginzburg orbifolds with the permutation symmetries of variables. We calculate the formula of the Poincare polynomial for a certain loop polynomial orbifoldized by a semidirect product of a diagonal symmetry group and cyclic permutation group and check that the generalization of Berglund–Hubsch transpose gives mirror symmetric pairs for these cases.

中文翻译：

---

具有环型势的非阿贝尔 Landau-Ginzburg orbifolds 的镜像对称

摘要 我们研究了具有变量置换对称性的Landau-Ginzburg orbifolds 的双梯度向量空间结构。我们计算由对角对称群和循环置换群的半直积或二重化的某个循环多项式的庞加莱多项式的公式，并检查 Berglund-Hubsch 转置的推广是否为这些情况提供了镜像对称对。