  We establish a formula of the large N factorization of the modular S-matrix
for the coupled representations in U(N) Chern-Simons theory. The formula was
proposed by Aganagic, Neitzke and Vafa, based on computations involving the
conifold transition. We present a more rigorous proof that relies on the
universal character for rational representations and an expression of the
modular S-matrix in terms of the specialization of characters.
