On algebraic structures underlying the rational Kashiwara-Miwa-type models

Abstract: The rational Kashiwara-Miwa model is an example of an Ising-type integrable model of the statistical physics, related to the six-vertex trigonometric $R$-matrix. Two-spin edge weights of the model are expressed in the terms of $q$-products, its spins are arbitrary integers, and $|q|<1$. We discuss in this paper the algebraic structures underlying the model, in particular its relation to the $q$-oscillator algebra, to representations of the $q$-oscillator algebra and to the co-product of the $q$-oscillator algebra.