Related papers: Integrability and Fusion Algebra for Quantum Mappi…
Given a finite-dimensional, complex simple Lie algebra we exhibit an integral form for the universal enveloping algebra of its map algebra, and an explicit integral basis for this integral form. We also produce explicit commutation formulas…
We find a method to construct iteratively from a non-degenerate involutive set-theoretic solution of the Yang-Baxter equation an infinite family of very large non-degenerate involutive set-theoretic solutions. In case the initial solution…
Integrable quantum field models are known to exist mostly in one space-dimension. Exploiting the concept of multi-time in integrable systems and a Lax matrix of higher scaling order, we construct a novel quantum field model in quasi-two…
We present a construction of integrable hierarchies without or with boundary, starting from a single R-matrix, or equivalently from a ZF algebra. We give explicit expressions for the Hamiltonians and the integrals of motion of the hierarchy…
In the 1990s, Drinfel'd proposed the study of set-theoretical solutions to the quantum Yang-Baxter equation, initiating a line of research that has since garnered substantial attention and led to notable developments in algebra,…
We present a systematic approach for constructing steady state density operators of Markovian dissipative evolution for open quantum chain models with integrable bulk interaction and boundary incoherent driving. The construction is based on…
We resolve the `baxterization' problem with the help of the automorphism group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations. This infinite group of symmetries is realized as a non-linear (birational) Coxeter group…
We present solutions for the (constant and spectral-parameter) Yang-Baxter equations and Yang-Baxter systems arising from algebra structures and discuss about their symmetries. In the last section, we present some applications.
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 construct spectral parameter dependent R-matrices for the quantized enveloping algebras of twisted affine Lie algebras. These give new solutions to the spectral parameter dependent quantum Yang-Baxter equation.
The Yang-Baxter equation and it's various forms have applications in many fields, including statistical mechanics, knot theory, and quantum information. Unitary solutions of the braided Yang-Baxter equation are of particular interest as…
The spectral problem for an integrable system of particles satisfying the fusion rules of $SU(3)_k$ is expressed in terms of exact inversion identities satisfied by the commuting transfer matrices of the integrable fused $A_2^{(1)}$…
This paper presents an explicit correspondence between two different types of integrable equations; the quantum Yang-Baxter equation in its star-triangle relation form, and the classical 3D-consistent quad equations in the…
The algebraic structures related with integrable structure of superconformal field theory (SCFT) are introduced. The SCFT counterparts of Baxter's Q-operator are constructed. The fusion-like relations for the transfer-matrices in different…
This article, based on the author's PhD thesis, reviews recent advancements in the field of quantum integrability, in particular the separation of variables (SoV) program for high-rank integrable spin chains and the boost mechanism for…
This is a survey of the work of Seiberg and Witten on 4-dimensional N=2 supersymmetric Yang-Mills theory and of some of its recent extensions, written for mathematicians. The point of view is that of algebraic geometry and integrable…
We consider one dimensional block cellular automata, where the local update rules are given by Yang-Baxter maps, which are set theoretical solutions of the Yang-Baxter equations. We show that such systems are superintegrable: they possess…
The Yang-Baxterization R(z) of the trigonometric R-matrix is computed for the two-parameter quantum affine algebra of type A. Using the fusion procedure we construct all fundamental representations of the quantum algebra as wedge products…
Recent study suggests that there are natural connections between quantum information theory and the Yang--Baxter equation. In this paper, in terms of the generalized almost-complex structure and with the help of its algebra, we define the…
In this paper we introduce a new class of integrable 3D lattice models, possessing continuous families of commuting layer-to-layer transfer matrices. Algebraically, this commutativity is based on a very special construction of local…