Universal R operator with deformed conformal symmetry

Abstract

We study the general solution of the Yang-Baxter equation with deformed $sl(2)$ symmetry. The universal R operator acting on tensor products of arbitrary representations is obtained in spectral decomposition and in integral forms. The results for eigenvalues, eigenfunctions and integral kernel appear as deformations of the ones in the rational case. They provide a basis for the construction of integrable quantum systems generalizing the XXZ spin models to the case of arbitrary not necessarily finite-dimensional representations on the sites.

18 pages LaTex, revised, to be publ. in Nucl. Phys

References in corpus (4)

• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
• Universal R-matrix as integral operator
• Parton interactions in the Bjorken limit of QCD

Cited by in corpus (11)

• Quasilocal charges in integrable lattice systems
• Families of quasi-local conservation laws and quantum spin transport
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Matrix product solutions of boundary driven quantum chains
• Yang-Baxter R operators and parameter permutations
• Exterior integrability: Yang-Baxter form of nonequilibrium steady state density operator
• Quantum group approach to steady states of boundary-driven open quantum systems
• Baxter Q-operators of the XXZ chain and R-matrix factorization
• Correlators with $s{\ell }_2$ Yangian symmetry
• Jordan-Schwinger Representations and Factorised Yang-Baxter Operators
• Universal R operator with Jordanian deformation of conformal symmetry