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Related papers: On higher spin Uq(sl_2)-invariant R-matrices

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We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary…

Mathematical Physics · Physics 2016-08-09 Sabina Alazzawi , Gandalf Lechner

We find a new $4\times4$ solution to the $osp_q(1|2)$-invariant Yang-Baxter equation with simple dependence on the spectral parameter and propose $2\times 2$ matrix expressions for the corresponding Lax operator. The general inhomogeneous…

Mathematical Physics · Physics 2009-03-11 D. Karakhanyan , Sh. Khachatryan

The intertwiner of the quantized coordinate ring $A_q(sl_3)$ is known to yield a solution to the tetrahedron equation. By evaluating their $n$-fold composition with special boundary vectors we generate series of solutions to the Yang-Baxter…

Mathematical Physics · Physics 2015-03-30 Atsuo Kuniba , Masato Okado

We present an uniform construction of the solution to the Yang- Baxter equation with the symmetry algebra $s\ell(2)$ and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator acting in the…

High Energy Physics - Theory · Physics 2008-11-26 S. Derkachov , D. Karakhanyan , R. Kirschner

In the past years, there have been tremendous advances in the field of planar N=4 super Yang-Mills scattering amplitudes. At tree-level they were formulated as Grassmannian integrals and were shown to be invariant under the Yangian of the…

High Energy Physics - Theory · Physics 2015-03-24 Nils Kanning , Yumi Ko , Matthias Staudacher

An explicit quantization is given of certain skew-symmetric solutions of the classical Yang-Baxter, yielding a family of $R$-matrices which generalize to higher dimensions the Jordanian $R$-matrices. Three different approaches to their…

Quantum Algebra · Mathematics 2007-05-23 Robin Endelman , Timothy J. Hodges

We perform an explicit two-loop calculation of the dilatation operator acting on single trace Wilson operators built from holomorphic scalar fields and an arbitrary number of covariant derivatives in N=2 and N=4 supersymmetric Yang-Mills…

High Energy Physics - Theory · Physics 2008-11-26 A. V. Belitsky , G. P. Korchemsky , D. Müller

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)…

High Energy Physics - Theory · Physics 2009-01-23 Vladimir V. Bazhanov , Zengo Tsuboi

By using a class of `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of $SU(M)$ Haldane-Shastry (HS) spin…

solv-int · Physics 2009-10-31 B. Basu-Mallick

There is remarkable relation between self-dual Yang-Mills and self-dual Einstein gravity in four Euclidean dimensions. Motivated by this we investigate the Spin(7) and G_2 invariant self-dual Yang-Mills equations in eight and seven…

High Energy Physics - Theory · Physics 2009-11-07 Konstadinos Sfetsos

New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for $sl(2,\mathbb{C})$. These solutions are…

Mathematical Physics · Physics 2018-02-14 Andrey Smirnov

A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an…

High Energy Physics - Theory · Physics 2009-10-31 J. M. Maillet , V. Terras

Supersymmetry algebras can be used to obtain algebraic expressions for constant Yang-Baxter solutions, also known as braid group generators. This was done for non-invertible braid operators in \cite{maity2025non}. In this work we extend…

High Energy Physics - Theory · Physics 2025-08-07 Somnath Maity , Pramod Padmanabhan , Jarmo Hietarinta , Vladimir Korepin

We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…

Mathematical Physics · Physics 2015-06-23 A. A. Ovchinnikov

We consider the N-site U_{q}(gl(N)) integrable spin chain with periodic and open diagonal soliton-preserving boundary conditions. By employing analytical Bethe ansatz techniques we are able to determine the spectrum and the corresponding…

Mathematical Physics · Physics 2009-11-11 D. Arnaudon , N. Crampe , A. Doikou , L. Frappat , E. Ragoucy

We describe several methods of constructing R-matrices that are dependent upon many parameters, for example unitary R-matrices and R-matrices whose entries are functions. As an application, we construct examples of R-matrices with…

Rings and Algebras · Mathematics 2017-11-10 Agata Smoktunowicz , Alicja Smoktunowicz

The Yang-Baxter Equation (YBE) plays a crucial role for studying integrable many-body quantum systems. Many known YBE solutions provide various examples ranging from quantum spin chains to superconducting systems. Models of solvable…

Quantum Physics · Physics 2024-11-19 Alexander. S. Garkun , Suvendu K. Barik , Aleksey K. Fedorov , Vladimir Gritsev

We study higher spin (pure and mixed spin) representations of the Yangian of $\mathfrak{sl}_2$. We provide a geometric realization in terms of the critical cohomology of representations of the quiver with potential of Bykov and Zinn-Justin…

Representation Theory · Mathematics 2026-01-05 Yaping Yang , Paul Zinn-Justin

We obtain inequivalent classical r-matrices of the $osp(1|2)$ Lie superalgebra as real solutions of the graded (modified) classical Yang-Baxter equation, in such a way that the corresponding automorphism transformation is employed. Then,…

High Energy Physics - Theory · Physics 2025-12-10 Ali Eghbali , Yaghoub Samadi , Adel Rezaei-Aghdam

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…

Mathematical Physics · Physics 2011-06-13 Vladimir V. Bazhanov , Rouven Frassek , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher