  We study superstring propagations on the Calabi-Yau manifold which develops
an isolated ADE singularity. This theory has been conjectured to have a
holographic dual description in terms of N=2 Landau-Ginzburg theory and
Liouville theory. If the Landau-Ginzburg description precisely reflects the
information of ADE singularity, the Landau-Ginzburg model of $D_4,E_6,E_8$ and
Gepner model of $A_2\otimes A_2, A_2\otimes A_3, A_2\otimes A_4$ should give
the same result. We compute the elements of $D_4,E_6,E_8$ modular invariants
for the singular Calabi-Yau compactification in terms of the spectral flow
invariant orbits of the tensor product theories with the theta function which
encodes the momentum mode of the Liouville theory. Furthermore we find the
interesting identity among characters in minimal models at different levels. We
give the complete proof for the identity.
