On Inner Product on Conformal

This is the second part of the paper (the rst part is published in Journal of AMS 9 1135. In the rst part, we deened for every modular tensor category (MTC) inner products on the spaces of morphisms and proved that the inner product on the space Hom(L X i X i ; U) is modular invariant. Also, we have shown that in the case of the MTC arising from the representations of the quantum group U q sl n at roots of unity and U being a symmetric power of the fundamental representation , this inner product coincides with so-called Macdonald's inner product on symmetric polynomials. In this paper, we apply the same construction to the MTC coming from the integrable representations of aane Lie algebras. In this case our construction immediately gives a hermitian form on the spaces of conformal blocks, and this form is modular invariant (Warning: we cannot prove that it is positive dee-nite). We show that this form can be rewritten in terms of asymptotics of KZ equations, and calculate it for sl 2 , in which case the formula is a natural aane analogue of Macdonald's inner product identities. We also formulate as a conjecture similar formula for sl n .