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Related papers: $A_{n-1}^{(1)}$ Reflection K-Matrices

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We present a new solution to the reflection equation associated with a coideal subalgebra of $U_q(A^{(1)}_{n-1})$ in the symmetric tensor representations and their dual. Elements of the $K$ matrix are expressed by a matrix product formula…

Mathematical Physics · Physics 2019-12-03 Atsuo Kuniba , Masato Okado , Akihito Yoneyama

We obtain the reflection matrices for the scattering of elementary magnons from certain open boundaries, corresponding to open strings ending on D7 and D5 branes in $AdS_5\times S^5$. In each case we consider two possible orientations for…

High Energy Physics - Theory · Physics 2011-05-24 D. H. Correa , C. A. S. Young

In this paper we compute the most general nondiagonal reflection matrices of the RSOS/SOS models and hard hexagon model using the boundary Yang-Baxter equations. We find new one-parameter family of reflection matrices for the RSOS model in…

solv-int · Physics 2009-10-30 C. Ahn , C. K. You

We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and non-diagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS…

High Energy Physics - Theory · Physics 2009-10-28 C. Ahn , W. M. Koo

We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class…

Mathematical Physics · Physics 2015-05-14 M. J. Martins , C. S. Melo

We propose explicit expressions for the boundary reflection matrices of the ${\cal A}_m+(r,s)$ series of massive scattering theories, obtained by perturbing the ${\cal A}_m$ unitary minimal models with $(r,s)$ boundary conditions with both…

High Energy Physics - Theory · Physics 2025-12-25 Zoltan Bajnok , Rafael I. Nepomechie , Paul A. Pearce

Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such…

Quantum Algebra · Mathematics 2007-05-23 Alexander Odesskii , Vladimir Sokolov

The reflection equations (RE) are a consistent extension of the Yang-Baxter equations (YBE) with an addition of one element, the so-called reflection matrix or $K$-matrix. For example, they describe the conditions for factorizable…

High Energy Physics - Theory · Physics 2014-11-18 P. P. Kulish , R. Sasaki

The main aim of this paper is to determine reflections to bijective and non-degenerate solutions of the Yang-Baxter equation, by exploring their connections with their derived solutions. This is motivated by a recent description of left…

Quantum Algebra · Mathematics 2025-05-02 Andrea Albano , Marzia Mazzotta , Paola Stefanelli

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…

Quantum Algebra · Mathematics 2015-06-26 K. A. Dancer , P. S. Isaac , J. Links

We present most general one-parametric solutions of the Yang-Baxter equations (YBE) for one spectral parameter dependent $R_{ij}(u)$-matrices of the six- and eight-vertex models, where the only constraint is the particle number conservation…

Mathematical Physics · Physics 2013-05-09 Sh. Khachatryan , A. Sedrakyan

We introduce An(1) (n=1,2,...) affine quiver matrix model by simply adopting the extended Cartan matrices as incidence matrices and study its finite N Schwinger-Dyson equations as well as their planar limit. In the case of n=1, we extend…

High Energy Physics - Theory · Physics 2011-08-04 Hiroshi Itoyama , Takeshi Oota

The set-theoretical reflection equation and its solutions, the reflection maps, recently introduced by two of the authors, is presented in general and then applied in the context of quadrirational Yang-Baxter maps. We provide a method for…

Mathematical Physics · Physics 2013-02-22 V. Caudrelier , N. Crampe , Q. C. Zhang

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…

Mathematical Physics · Physics 2015-03-02 D. Chicherin , S. Derkachov

We study solutions of the parametric set-theoretic reflection equation from an algebraic perspective by employing recently derived generalizations of the familiar shelves and racks, called parametric (p)-shelves and racks. Generic…

Rings and Algebras · Mathematics 2026-02-13 Anastasia Doikou , Marzia Mazzotta , Paola Stefanelli

We investigate certain bases of Hecke algebras defined by means of the Yang-Baxter equation, which we call Yang-Baxter bases. These bases are essentially self-adjoint with respect to a canonical bilinear form. In the case of the degenerate…

q-alg · Mathematics 2008-02-03 Alain Lascoux , Bernard Leclerc , Jean-Yves Thibon

In this paper we investigate trigonometric vertex models associated with solutions of the Yang-Baxter equation which are invariant relative to q-deformed superalgebras sl(r|2m)^(2), osp(r|2m)^(1) and osp(r=2n|2m)^(2). The associated…

Exactly Solvable and Integrable Systems · Physics 2011-04-26 W. Galleas , M. J. Martins

One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to…

Mathematical Physics · Physics 2024-03-25 Alec Cooper , Bart Vlaar , Robert Weston

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…

High Energy Physics - Theory · Physics 2009-10-30 M. Moriconi , K. Schoutens

We construct nonstandard finite-dimensional representations of type C affine Hecke algebra from the viewpoint of quantum integrable models. There exists two classes of nonstandard solutions to the Yang-Baxter equation called the…

Quantum Algebra · Mathematics 2015-07-07 Kohei Motegi