Yang-Baxter R operators and parameter permutations

Abstract

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 tensor product of two representations of the symmetry algebra with arbitrary spins ${\ell }_1$ and ${\ell }_2$ is built in terms of products of three basic operators ${\mathcal{S}}_1,{\mathcal{S}}_2,{\mathcal{S}}_3$ which are constructed explicitly. They have the simple meaning of representing elementary permutations of the symmetric group ${\mathfrak{S}}_4$, the permutation group of the four parameters entering the RLL-relation.

22 pages LaTex, comments added, version to be published in Nucl. Phys. B

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Cited by in corpus (17)

• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• Baxter operators with deformed symmetry
• Elliptic hypergeometric functions
• New elliptic solutions of the Yang-Baxter equation
• From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation
• Intertwining operators for Sklyanin algebra and elliptic hypergeometric series
• Correlators with $s{\ell }_2$ Yangian symmetry
• Jordan-Schwinger Representations and Factorised Yang-Baxter Operators
• The hyperbolic modular double and the Yang-Baxter equation
• The R-operator for Modular Double
• Iterative construction of $U_q(s\ell (n+1))$ representations and Lax matrix factorisation
• Finite-dimensional representations of the elliptic modular double
• Factorization of R-matrix and Baxter's Q-operator
• Matrix Bailey Lemma and the Star-Triangle Relation
• Yangian symmetry applied to Quantum chromodynamics
• Matrix factorization for solutions of the Yang-Baxter equation
• QCD at high energies and Yangian symmetry