Yangian, Truncated Yangian and Quantum Integrable Systems

TL;DR

This paper explores the algebraic structures of Yangian and truncated Yangian derived from RTT relations, linking them to integrable models and specific physical systems like the Goryachev-Chaplygin gyrostat.

Contribution

It introduces the connection between Yangian structures and integrable systems, including the extension to trigonometric cases and their physical applications.

Findings

Yangian generates long-range interaction models

Truncated Yangian relates to Goryachev-Chaplygin gyrostat

Trigonometric extension of the gyrostat is demonstrated

Abstract

Based on the RTT relation for a given rational $R$-matrix the {\em Yangian} and truncated {\em Yangian} are discussed. The former can be used to generate the long-range interaction models, whereas the latter can be related to the Goryachev-Chaplygin(GC) gyrostat. The trigonometric extension of the Goryachev-Chaplygin gyrostat has also been shown.