On explicit free field realizations of current algebras

We construct the explicit free field representations of the current algebras $so(2n)_k$, $so(2n+1)_k$ and $sp(2n)_k$ for a generic positive integer $n$ and an arbitrary level $k$. The corresponding energy-momentum tensors and screening currents of the first kind are also given in terms of free fields.Comment: Latex file, 25 page

Multiple reference states and complete spectrum of the ZnZ_n Belavin model with open boundaries

The multiple reference state structure of the $\Z_n$ Belavin model with non-diagonal boundary terms is discovered. It is found that there exist $n$ reference states, each of them yields a set of eigenvalues and Bethe Ansatz equations of the transfer matrix. These $n$ sets of eigenvalues together constitute the complete spectrum of the model. In the quasi-classic limit, they give the complete spectrum of the corresponding Gaudin model.Comment: Latex file, 24 page

Q-operator and T-Q relation from the fusion hierarchy

We propose that the Baxter $Q$-operator for the spin-1/2 XXZ quantum spin chain is given by the $j\to \infty$ limit of the transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. Applying this observation to the open chain with general (nondiagonal) integrable boundary terms, we obtain from the fusion hierarchy the $T$-$Q$ relation for {\it generic} values (i.e. not roots of unity) of the bulk anisotropy parameter. We use this relation to determine the Bethe Ansatz solution of the eigenvalues of the fundamental transfer matrix. This approach is complementary to the one used recently to solve the same model for the roots of unity case.Comment: Latex file, 12 pages; V2, misprints corrected and references adde

Determinant Representation of Correlation Functions for the Uq(gl(1∣1))U_q(gl(1|1)) Free Fermion Model

With the help of the factorizing $F$-matrix, the scalar products of the $U_q(gl(1|1))$ free fermion model are represented by determinants. By means of these results, we obtain the determinant representations of correlation functions of the model.Comment: Latex File, 20 pages, V.3: some discussions are added, V.4 Reference update, this version will appear in J. Math. Phy