B_{n}^{(1)} and A_{2n}^{(2)}reflection K-matrices

Abstract

We investigate the regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the $B_n^{(1)}$ and $A_{2n}^{(2)}$ affine Lie algebras. In both class of models we find two general solutions with $n+1$ free parameters. In addition, we have find $2n-1$ diagonal solutions for $B_n^{(1)}$ models and $2n+1$ diagonal solutions for models. It turns out that for each $B_n^{(1)}$ model there exist a diagonal K-matrix with one free parameter. Moreover, a three free parameter general solution exists for the $B_1^{(1)}$ model which is the vector representation for the Zamolodchikov-Fateev model.

14 pages, LaTex

References in corpus (13)

• Quantum Inverse Scattering Method and Correlation Functions
• Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
• Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''
• Solutions of the reflection equation for face and vertex models associated with $A_n^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ and $A_n^{(2)}$
• Reflection K-Matrices for 19-Vertex Models
• Boundary quantum group generators of type A
• Reflection K-Matrices of the 19-Vertex Model and XXZ Spin-1 Chain with General Boundary Terms
• Non-diagonal solutions to reflection equations in $su(n)$ spin chains
• Integrability of the $D_n^2$ vertex models with open boundary
• $A_{n-1}^{(1)}$ Reflection K-Matrices
• Boundary K-matrix for the quantum Mikhailov-Shabat model
• Classification of Solutions to Reflection Equation of Two-Component Systems
• D_{n+1}^(2) Reflection K-matrices

Cited by in corpus (10)

• On $A_{n-1}^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)},A_{2n}^{(2)},A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices
• $C_n^{(1)}$, $D_n^{(1)}$ and $A_{2n-1}^{(2)}$ reflection K-matrices
• Surveying the quantum group symmetries of integrable open spin chains
• The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains
• Solutions of the reflection equations for the $U_q[G_2]$ vertex model
• The spectrum of quantum-group-invariant transfer matrices
• The algebraic Bethe ansatz for open vertex models
• Quantum group symmetries and completeness for A_{2n}^(2) open spin chains
• The algebraic Bethe ansatz for open A_{2n}^{(2)} vertex model
• Spin chains with boundary inhomogeneities