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

TL;DR

This paper explores the algebraic foundations of the rational Kashiwara-Miwa model, linking it to the $q$-oscillator algebra and its representations, enhancing understanding of its integrable structure.

Contribution

It reveals the algebraic structures, especially the $q$-oscillator algebra and its co-product, underlying the rational Kashiwara-Miwa model.

Findings

Connection between the model and $q$-oscillator algebra established

Representation theory of the $q$-oscillator algebra applied

Insights into the algebraic structure of integrable models obtained

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.