Related papers: B_{n}^{(1)} and A_{2n}^{(2)}reflection K-matrices
In this paper we discuss representations of the Birman-Wenzl-Murakami algebra as well as of its dilute extension containing several free parameters. These representations are based on superalgebras and their baxterizations permit us to…
We obtain two series of spectral parameter dependent solutions to the generalized Yang-Baxter equations (GYBE), for definite types of $N_1^2\times N_2^2$ matrices with general dimensions $N_1$ and $N_2$. Appropriate extensions are presented…
Given an arbitrary choice of two sets of nonzero Boltzmann weights for $n$-color lattice models, we provide explicit algebraic conditions on these Boltzmann weights which guarantee a solution (i.e., a third set of weights) to the…
We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a…
We construct $R$-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They…
The symmetries, especially those related to the $R$-transformation, of the reflection equation(RE) for two-component systems are analyzed. The classification of solutions to the RE for eight-, six- and seven-vertex type $R$-matrices is…
Integral formulae for the correlation functions of the XYZ model with a boundary are calculated by mapping the model to the bosonized boundary SOS model. The boundary K-matrix considered here coincides with the known general solution of the…
A generalization of the Yang-Baxter equation is proposed. It enables to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit…
We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sl_2, the…
We present a generalization the G. Letzter's theory of quantum symmetric pairs of semisimple Lie algebras for the case of quantum affine algebras. We then study solutions of the reflection equation for the quantum affine algebras sl(2) and…
We consider finite-dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced R-operators…
The type-I simple Lie-superalgebras are $sl(m|n)$ and $osp(2|2n)$. We study the quantum deformations of their untwisted affine extensions $U_q(sl(m|n)^{(1)})$ and $U_q(osp(2|2n)^{(1)})$. We identify additional relations between the simple…
We present a generalization of the theory of quantum symmetric pairs as developed by Kolb and Letzter. We introduce a class of generalized Satake diagrams that give rise to (not necessarily involutive) automorphisms of the second kind of…
Many of the known solutions of the Yang-Baxter equation, which are related to solvable lattice models of vertex- and IRF-type, yield representations of the Birman-Wenzl-Murakami algebra. From these, representations of a two-colour…
We present particularly simple new solutions to the Yang--Baxter equation arising from two--dimensional cyclic representations of quantum $SU(2)$. They are readily interpreted as scattering matrices of relativistic objects, and the quantum…
We survey the matrix product solutions of the Yang-Baxter equation obtained recently from the tetrahedron equation. They form a family of quantum $R$ matrices of generalized quantum groups interpolating the symmetric tensor representations…
Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter…
We describe the construction of trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two irreducible representations of a quantum algebra $U_q(\G)$. Our method is a generalization of the tensor product…
In this paper we investigate the algebraic geometric nature of a solution of the Yang-Baxter equation based on the quantum deformation of the centrally extended $sl(2|2)$ superalgebra proposed by Beisert and Koroteev \cite{BEKO}. We derive…
A unified approach is applied in the consideration of the multi-parametric (colored) Yang-Baxter equations (YBE) and the usual YBE with two-parametric R-matrices, relying on the existence of the arbitrary functions in the general solutions.…