Temperley-Lieb K-matrices

2011/01/03 by A. Lima-Santos, Lima-Santos, A.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1101.0540

Abstract

This work concerns to the studies of boundary integrability of the vertex models from representations of the Temperley-Lieb algebra associated with the quantum group \cal U_q[X_n] for the affine Lie algebras X_n = A₁⁽¹⁾, B_n⁽¹⁾, C_n⁽¹⁾ and D_n⁽¹⁾. A systematic computation method is used to constructed solutions of the boundary Yang-Baxter equations. We find a 2n²+1 free parameter solution for A₁⁽¹⁾ spin-(n-1/2) and C_n⁽¹⁾ vertex models. It turns that for A₁⁽¹⁾ spin-n, B_n⁽¹⁾ and D_n⁽¹⁾ vertex models, the solution has 2n²+2n+1 free parameters.

Related

• Calibrated representations of two boundary Temperley-Lieb algebras
• Integrability of the Six-Vertex model and the Yang-Baxter Groupoid
• Embedding integrable spin models in solvable vertex models on the square lattice
• Integrable Vertex Models with General Twists
• Integrable XYZ spin chain with boundaries