Related papers: Transfer matrix eigenvalues of the anisotropic mul…
In the framework of the graded quantum inverse scattering method (QISM), we obtain the eigenvalues and eigenvectors of the supersymmetric $t-J$ model with reflecting boundary conditions in FFB background. The corresponding Bethe ansatz…
We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…
Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice…
Exact quantum integrability is established for a class of multi-chain electron models with correlated hopping and spin models with interchain interactions, by constructing the related Lax operators and R-matrices through twisting and gauge…
We study involutive set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2. These solutions happen to fall into two classes -- distributive ones and non-distributive ones. The distributive ones can be effectively…
It is well known that, given a Yang-Baxter map, there is a hierarchy of commuting transfer maps, which arise out of the consideration of initial value problems. In this paper, we show that one can construct invariants of the transfer maps…
We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter…
The hierarchy of commuting maps related to a set-theoretical solution of the quantum Yang-Baxter equation (Yang-Baxter map) is introduced. They can be considered as dynamical analogues of the monodromy and/or transfer-matrices. The general…
We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider…
We study the Yangian of the sl(2|1) Lie superalgebra in a multi-parametric four-dimensional representation. We use Drinfeld's second realization to independently rederive the R-matrix, and to obtain the antiparticle representation, the…
The north-west corner transfer matrix of an inhomogeneous integrable vertex model constructed from the vector representation of $U_q\bigl(sl(2/1)\bigr)$ and its dual is investigated. In the limit $q\to0$, the spectrum can be obtained. Based…
We consider a special class of quantum non-dynamical $R$-matrices in the fundamental representation of ${\rm GL}_N$ with spectral parameter given by trigonometric solutions of the associative Yang-Baxter equation. In the simplest case $N=2$…
By means of an algebraic Bethe ansatz approach we study the Zamolodchikov-Fateev and Izergin-Korepin vertex models with non-diagonal boundaries, characterized by reflection matrices with an upper triangular form. Generalized Bethe vectors…
We give an explicit formula for the exchange matrix correponding to the tensor product of two copies of the natural (standard) evaluation representation of the quantum group associated to the affine Lie algebra of sl(n+1). Then we calculate…
We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra $gl_N$. The models are defined on a tensor product irreducible $gl_N$-modules. For each model, there exist $N$ one-parameter families of commuting…
We extend our recent work on set-theoretic solutions of the Yang-Baxter or braid relations with new results about their automorphism groups, strong twisted unions of solutions and multipermutation solutions. We introduce and study graphs of…
The general expression for the local matrix $L(\theta)$ of a quantum chain with the site space in any representation of $su(3)$ is obtained. This is made by generalizing $L(\theta)$ from the fundamental representation and imposing the…
We generalise the fusion procedure for the $A_{\n-1}^{(1)}$ open spin chain ($\n>2$) and we show that the transfer matrix satisfies a crossing property. We use these results to solve the $A_{\n-1}^{(1)}$ open spin chain with $U_{q}…
Whereas the tools to determine the eigenvalues of the eight-vertex transfer matrix T are well known there has been until recently incomplete knowledge about the eigenvectors of T. We describe the construction of eigenvectors of T…
The theory of the set-theoretic Yang-Baxter equation is reviewed from a purely algebraic point of view. We recall certain algebraic structures called shelves, racks and quandles. These objects satisfy a self-distributivity condition and…