Related papers: Temperley-Lieb K-matrices
In this paper we present Affine.m - program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. Algorithms are based upon the properties of weights and Weyl symmetry.…
Boundary integrable models with N=2 supersymmetry are considered. For the simplest boundary N=2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in…
Affine quantum groups are certain pseudo-quasitriangular Hopf algebras that arise in mathematical physics in the context of integrable quantum field theory, integrable quantum spin chains, and solvable lattice models. They provide the…
Using the previous obtained universal $R$-matrix for the quantized nontwisted affine Lie algebras $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, we determine the explicitly spectral-dependent universal $R$-matrix for the corresponding quantum Lie…
We complete our analysis of the Temperley-Lieb subproduct systems, which define quantum analogues of Arveson's $2$-shift, by extending the main results of the previous paper to the general parameter case. Specifically, we show that the…
Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically…
We present a systematic method to introduce free parameters in sets of mutually unbiased bases. In particular, we demonstrate that any set of m real mutually unbiased bases in dimension N>2 admits the introduction of (m-1)N/2 free…
We study two-dimensional integrable $N=1$ supersymmetric theories (without topological charges) in the presence of a boundary. We find a universal ratio between the reflection amplitudes for particles that are related by supersymmetry and…
We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r index of…
Integrable open-boundary condition for the q-deformed Essler-Korepin-Schoutens extended Hubbard model of strongly correlated electrons, are studied in the framework of the boundary quantum inverse scattering method. Diagonal boundary…
It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract,normed C*-algebra. In the course we also recover an intermediate connection with the words of a Dyck language and Tempereley-Lieb algebras for…
We study numerically the ODE/IM correspondence for untwisted affine Lie algebras associated with simple Lie algebras including exceptional type. We consider the linear problem obtained from the massless limit of that of the modified affine…
The affine Temperley-Lieb algebra $\mathsf{a}\hskip-1.8pt\mathsf{TL}_{N}(\beta)$ is an infinite-dimensional algebra parametrized by a number $\beta \in \mathbb{C}$ and an integer $N\in \mathbb{N}$. It naturally acts on…
Integrability conditions on local Hamiltonians for one-dimensional quantum systems to be free and interacting fermions are introduced. The definition of free fermion is the simultaneous satisfaction of the Yang-Baxter equation and Shastry's…
We study the dilute $A_2^{(2)}$ loop models on the geometry of a strip of width $N$. Two families of boundary conditions are known to satisfy the boundary Yang-Baxter equation. Fixing the boundary condition on the two ends of the strip…
We present the general diagonal and, in some cases, non-diagonal solutions of the boundary Yang-Baxter equation for a number of related interaction-round-a-face models, including the standard and dilute A_L, D_L and E_{6,7,8} models.
We investigate integrable boundary conditions (BCs) for the principal chiral model on the half-line, and rational solutions of the boundary Yang-Baxter equation (BYBE). In each case we find a connection with (type I, Riemannian, globally)…
For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these…
A new class of $A^{(1)}_n$ integrable lattice models is presented. These are interaction-round-a-face models based on fundamental nimrep graphs associated with the $A^{(1)}_n$ conjugate modular invariants, there being a model for each value…
Using a modified version of the tetrahedron equations we construct a new family of $N$-state three-dimensional integrable models with commuting two-layer transfer-matrices. We investigate a particular class of solutions to these equations…