Rational and polynomial representations of Yangians

TL;DR

This paper introduces rational and polynomial representations of the Yangian for the general linear Lie algebra, providing a classification and explicit realizations of all irreducible rational representations.

Contribution

It offers a new framework for understanding Yangian representations by classifying and explicitly constructing all irreducible rational cases.

Findings

Classification of all irreducible rational Yangian representations

Explicit realizations of these representations

Introduction of natural classes of rational and polynomial representations

Abstract

We define natural classes of rational and polynomial representations of the Yangian of the general linear Lie algebra. We also present the classification and explicit realizations of all irreducible rational representations of the Yangian.