Equivalences between three presentations of orthogonal and symplectic Yangians

TL;DR

This paper establishes the equivalence of three different presentations of Yangians associated with orthogonal and symplectic Lie algebras, providing a clearer understanding of their structure and classification of modules.

Contribution

It proves the equivalence of three presentations of orthogonal and symplectic Yangians, and relates different classification theorems for their finite-dimensional irreducible modules.

Findings

Proved equivalence of two presentations of $Y(rak{g})$

Established equivalence with a third presentation for orthogonal and symplectic cases

Provided explicit correspondence between classification theorems

Abstract

We prove the equivalence of two presentations of the Yangian $Y(\mathfrak{g})$ of a simple Lie algebra $\mathfrak{g}$ and we also show the equivalence with a third presentation when $\mathfrak{g}$ is either an orthogonal or a symplectic Lie algebra. As an application, we obtain an explicit correspondence between two versions of the classification theorem of finite-dimensional irreducible modules for orthogonal and symplectic Yangians.