Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: Bazhanov, Vladimir V., Kotousov, Gleb A., Koval, Sergii M., Lukyanov, Sergei L.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211163
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model. Vladimir V. Bazhanov, Gleb A. Kotousov, Sergii M. Koval and Sergei L. Lukyanov. SIGMA 17 (2021), 025, 29 pages

The inhomogeneous six-vertex model is a 2 multiparametric integrable statistical system. In the scaling limit, it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions, the model possesses U(1) invariance. In this paper, we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of , , and as well as translational invariance. The special properties of the lattice system that possesses an additional ᵣ invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model.