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Related papers: Baxter operators with deformed symmetry

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Enhanced Yang-Baxter operators give rise to invariants of oriented links. We expand the enhancing method to generalized Yang-Baxter operators. At present two examples of generalized Yang-Baxter operators are known and recently three types…

Geometric Topology · Mathematics 2012-02-20 Seung-moon Hong

We study the deformations of a wide class of Yang-Baxter (YB) operators arising from Lie algebras. We relate the higher order deformations of YB operators to Lie algebra deformations. We show that the obstruction to integrating deformations…

Quantum Algebra · Mathematics 2024-03-18 Emanuele Zappala

Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with…

Mathematical Physics · Physics 2016-02-17 A. P. Isaev , D. Karakhanyan , R. Kirschner

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…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 A. E. Kovalsky , G. P. Pronko

We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators…

Mathematical Physics · Physics 2015-12-09 Rouven Frassek , Istvan M. Szecsenyi

Relying on a few lowest order perturbative calculations of anomalous dimensions of gauge invariant operators built from holomorphic scalar fields and an arbitrary number of covariant derivatives in maximally supersymmetric gauge theory, we…

High Energy Physics - Theory · Physics 2008-11-26 A. V. Belitsky

The Baxterization process for the dynamical Yang-Baxter equation is studied. We introduce the local dynamical Hecke ,Temperley-Lieb and Birman-Murakami-Wenzl operators, then by inserting spectral parameters, from each representation of…

Representation Theory · Mathematics 2024-01-23 Muze Ren

The spectral decomposition of regular Uq(sl_2)-invariant solutions of the Yang-Baxter equation is studied. An algorithm for finding all possible solutions of spin s is developed. It also allows to reconstruct the R-matrix from a given…

Quantum Algebra · Mathematics 2007-05-23 Andrei Bytsko

For any algebra two families of coloured Yang-Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang-Baxter equation. An open problem about a system of functional equations is stated. The matrix forms…

Quantum Algebra · Mathematics 2007-05-23 Florin F. Nichita , Deepak Parashar

It is shown that the transfer matrices of homogeneous sl(2) invariant spin chains with generic spin, both closed and open, are factorized into the product of two operators. The latter satisfy the Baxter equation that follows from the…

Exactly Solvable and Integrable Systems · Physics 2009-11-11 S. E. Derkachov , A. N. Manashov

We propose commuting sets of matrix-valued difference operators in terms of trigonometric ${\rm GL}(N|M)$-valued $R$-matrices thus providing quantum supersymmetric (and possibly anisotropic) spin Ruijsenaars-Macdonald operators. Two types…

Mathematical Physics · Physics 2024-03-05 M. Matushko , A. Zotov

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.

Quantum Algebra · Mathematics 2014-01-03 Florin F. Nichita , Bogdan P. Popovici

Integrable deformations of type IIB superstring theory on $\mathrm{AdS}_5\times S^5$ have played an important role over the last years. The Yang-Baxter deformation is a systematic way of generating such integrable deformations. Since its…

High Energy Physics - Theory · Physics 2020-12-02 Domenico Orlando , Susanne Reffert , Jun-ichi Sakamoto , Yuta Sekiguchi , Kentaroh Yoshida

We introduce non-degenerate solutions of the Yang-Baxter equation in the setting of symmetric monoidal categories. Our theory includes non-degenerate set-theoretical solutions as basic examples. However, infinite families of non-degenerate…

Quantum Algebra · Mathematics 2018-04-04 J. A. Guccione , J. J. Guccione , L. Vendramin

When the $q$-deformed creation and annihilation operators are used in a second quantization procedure, the algebra satisfied by basis vectors (orthogonal complete set) should be also deformed such as a field operator remains invariant under…

High Energy Physics - Theory · Physics 2017-02-01 Kazuhiko Odaka

Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the…

High Energy Physics - Theory · Physics 2015-06-17 D. Chicherin , S. Derkachov , R. Kirschner

Given a rack Q and a ring A, one can construct a Yang-Baxter operator c_Q: V tensor V --> V tensor V on the free A-module V = AQ by setting c_Q(x tensor y) = y tensor x^y for all x,y in Q. In answer to a question initiated by D.N. Yetter…

Quantum Algebra · Mathematics 2014-10-01 Michael Eisermann

We discuss homogeneous Yang-Baxter deformations of integrable sigma models in terms of twist operators. We show that the twist operators behave as the classical analogue of a Drinfeld twist, for all abelian and almost abelian deformations.…

High Energy Physics - Theory · Physics 2022-04-19 Stijn J. van Tongeren

In this paper we continue the study of $Q$-operators in the six-vertex model and its higher spin generalizations. In [1] we derived a new expression for the higher spin $R$-matrix associated with the affine quantum algebra…

Mathematical Physics · Physics 2014-07-16 Vladimir V. Mangazeev

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