Related papers: Solving Baxter's TQ-equation via representation th…
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are…
In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of $U_q(\hat{sl}_2)$ over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator…
A coloured braid group representation (CBGR) is constructed with the help of some modified universal ${\cal R}$-matrix, associated to $U_q(gl(2))$ quantised algebra. Explicit realisation of Faddeev-Reshetikhin-Takhtajan (FRT) algebra is…
We develop Yang-Baxter integrability structures connected with the quantum affine superalgebra Uq(\hat sl(2|1)). Baxter's Q-operators are explicitly constructed as supertraces of certain monodromy matrices associated with (q-deformed)…
We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the…
A new solution of the Yang-Baxter equation, that is related to the adjoint representation of the quantum enveloping algebra $U_{q}B_{2}$, is obtained by fusion formulas from a non-standard solution.
We construct solutions to the set-theoretic Yang-Baxter equation using braid group representations in free group automorphisms and their Fox differentials. The method resembles the extensions of groups and quandles.
Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any…
Quantum Toda lattice may solved by means of the Representation Theory of semisimple Lie groups, or alternatively by using the technique of the Quantum Inverse Scattering Method. A comparison of the two approaches, which is the purpose of…
In this paper we discuss some properties of Baxter's TQ equation for the eight-vertex elliptic Sklyanin algebra it its compact representation based on the elliptic Gamma-functions. As the main result, we establish the structure of the…
Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter TQ relations involving infinite-dimensional representations;…
In the present paper we describe the procedure of the Q-operators construction for the q-deformed model, described by the Lax operator, which is important to formulate the Bethe ansatz for the Sin-Gordon model. This Lax operator can also be…
Computational methods are an important tool for solving the Yang-Baxter equations(in small dimensions), for classifying (unifying) structures, and for solving related problems. This paper is an account of some of the latest developments on…
Solutions to the Yang-Baxter equation - an important equation in mathematics and physics - and their afforded braid group representations have applications in fields such as knot theory, statistical mechanics, and, most recently, quantum…
We propose that the Baxter's $Q$-operator for the XYZ quantum spin chain with open boundary conditions is given by the $j\to \infty$ limit of the corresponding transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. The…
The general rational solution of the Yang-Baxter equation with the symmetry algebra sl(2) can be represented as the product of the simpler building blocks denoted as R-operators. The R-operators are constructed explicitly and have simple…
We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-operator, the six-vertex transfer matrix and fusion matrices are…
We introduce a category $\mathcal O$ of representations of the elliptic quantum group associated with $\mathfrak{sl}_2$ with well-behaved $q$-character theory. We derive separation of variables relations for asymptotic representations in…
A computer algebra algoritm for solving the quantum Yang-Baxter equation is presented. It is based on the Taylor expansion of R-matrix which is developed up to the order \lambda^6. As an example the classification of 4x4 R-matrices is…
The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even…