Reflection $K$-matrices related to Temperley-Lieb $R$-matrices

Abstract

The general solutions of the reflection equation associated with Temperley-Lieb $R$-matrices are constructed. Their parametrization is defined and the Hamiltonians of corresponding integrable spin systems are given.

11 pages, no figures. References added and a few misprints corrected. To appear in Theoretical and Mathematical Physics (2011)

References in corpus (3)

• Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices
• Jordanian deformation of the open XXX-spin chain
• On the ${\mathcal{U}}_q[sl(2)]$ Temperley-Lieb reflection matrices

Cited by in corpus (12)

• Universal Bethe ansatz solution for the Temperley-Lieb spin chain
• Can a spin chain relate combinatorics to number theory?
• Shor-Movassagh chain leads to unusual integrable model
• Temperley-Lieb R-matrices from generalized Hadamard matrices
• Bethe ansatz for the Temperley-Lieb spin-chain with integrable open boundaries
• Algebraic Bethe ansatz for the Temperley-Lieb spin-1 chain
• Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 1. Super-analog of Reshetikhin formula
• Classification of Non-Affine Non-Hecke Dynamical R-Matrices
• Reflection matrices from Hadamard-type Temperley-Lieb R-matrices
• New Solutions to the Reflection Equation with Braces
• On the ${\mathcal{U}}_q[osp(1|2)]$ Temperley-Lieb model
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish