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The Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the off-diagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities and the asymptotic behaviors of the transfer matrix together allow us to construct the inhomogeneous T-Q relation and the associated Bethe ansatz equations. In the diagonal boundary limit, the reduced results coincide exactly with those obtained via other methods.
The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities amon
We use the quantum separation of variable (SOV) method to construct the eigenstates of the open XXZ chain with the most general boundary terms. The eigenstates in the inhomogeneous case are constructed in terms of solutions of a system of quadratic e
The generic quantum $tau_2$-model (also known as Baxter-Bazhanov-Stroganov (BBS) model) with periodic boundary condition is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix (solutions of the recur
We consider the Izergin-Korepin determinant [1] together with another determinant which was invented by Kuperberg [2]. He used these determinants to prove a formula for the total number of half-turn symmetric alternating sign matrices of even order c
We propose a convenient orthogonal basis of the Hilbert space for the Izergin-Korepin model (or the quantum spin chain associated with the $A^{(2)}_{2}$ algebra). It is shown that the monodromy-matrix elements acting on the basis take relatively simp