Higher rank generalization of 11-vertex rational R-matrix: IRF-Vertex relations and associative Yang-Baxter equation

Abstract

We study ${\mathrm{GL}}_N$ rational $R$-matrix, which turns into the 11-vertex $R$-matrix in the $N=2$ case. First, we describe its relations to dynamical and semi-dynamical $R$-matrices using the IRF-Vertex type transformations. As a by-product a new explicit form for ${\mathrm{GL}}_N$ $R$-matrix is derived. Next, we prove the quantum and the associative Yang-Baxter equations. A set of other $R$-matrix properties and $R$-matrix identities are proved as well.

21 pages

References in corpus (5)

• Relativistic Classical Integrable Tops and Quantum R-matrices
• Planck Constant as Spectral Parameter in Integrable Systems and KZB Equations
• Classical integrable systems and soliton equations related to eleven-vertex R-matrix
• Higher rank 1+1 integrable Landau-Lifshitz field theories from associative Yang-Baxter equation
• Relativistic elliptic matrix tops and finite Fourier transformations

Cited by in corpus (2)

• Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities
• Boltzmann weights and fusion procedure for the rational seven-vertex SOS model