Hodge Diamonds of the Landau-Ginzburg Orbifolds

Consider the pairs $(f,G)$ with f = f(x₁,,xN) being a polynomial defining a quasihomogeneous singularity and G being a subgroup of SL(N,C), preserving f. In particular, G is not necessary abelian. Assume further that G contains the grading operator jf and f satisfies the Calabi-Yau condition. We prove that the nonvanishing bigraded pieces of the B-model state space of $(f,G)$ form a diamond. We identify its topmost, bottommost, leftmost and rightmost entries as one-dimensional and show that this diamond enjoys the essential horizontal and vertical isomorphisms.