New non-diagonal solutions to the $a_n^{(1)}$ boundary Yang-Baxter equation

Abstract

Extending previous work on $a_2^{(1)}$, we present a set of reflection matrices, which are explicit solutions to the $a_n^{(1)}$ boundary Yang-Baxter equation. Unlike solutions found previously these are multiplet-changing $K$-matrices, and could therefore be used as soliton reflection matrices for affine Toda field theories on the half-line.

arXiv comment6 pages

References in corpus (1)

• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models

Cited by in corpus (15)

• Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• Boundary quantum group generators of type A
• Classification of reflection matrices related to (super) Yangians and application to open spin chain models
• Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions
• Non-diagonal solutions of the reflection equation for the trigonometric $A_{n-1}^{(1)}$ vertex model
• Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions
• Generalized q-Onsager algebras and boundary affine Toda field theories
• Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions
• Generalized q-Onsager Algebras and Dynamical K-matrices
• Matrix product solution to the reflection equation associated with a coideal subalgebra of $U_q(A_{n-1}^{(1)})$
• Integrable Models From Twisted Half Loop Algebras
• Solitons, Boundaries, and Quantum Affine Algebras
• Refection Matrices for the (n+1)(2n+1)- Vertex Models: Diagonal Solutions