We prove q-series identities between bosonic and fermionic representations of certain Virasoro characters.These identities include some of the conjectures made by the Stony Brook group as special cases. Our method is a direct application of Andrews' extensions of Bailey's lemma to recently obtained polynomial identities.⋆ Supported by the Australian Research Council.

We study the quantum Knizhnik-Zamolodchikov equation of level 0 associated with the spin 1/2 representation of U q ( sl 2 ). We find an integral formula for solutions in the case of an arbitrary total spin and |q| < 1. In the formula, different solutions can be obtained by taking different integral kernels with the cycle of integration being fixed.

A bosonization scheme of the q-vertex operators of U q ( sl 2 ) for arbitrary level is obtained. They act as intertwiners among the highest weight modules constructed in a bosonic Fock space. An integral formula is proposed for N-point functions and explicit calculation for two-point function is presented.

Presented are polynomial identities which imply generalizations of Euler and Rogers-Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by establishing a graphical one-to-one correspondence between those two kinds of restricted partitions.

Belavin's (ℤ/nℤ)-symmetric model is considered on the basis of bosonization of vertex operators in the A(1)n−1 model and vertex–face transformation. The corner transfer matrix (CTM) Hamiltonian of the (ℤ/nℤ)-symmetric model and tail operators are expressed in terms of bosonized vertex operators in the A(1)n−1 model. Correlation functions of the (ℤ/nℤ)-symmetric model can be obtained by using these objects, in principle. In particular, we calculate spontaneous polarization, which reproduces the result we obtained in 1993.