A Drinfeld-type presentation of the orthosymplectic Yangians

TL;DR

This paper develops a new Drinfeld-type presentation for the orthosymplectic Yangians by utilizing Gauss decomposition and a super-embedding theorem, advancing the algebraic understanding of these superalgebras.

Contribution

It introduces a novel Drinfeld-type presentation for orthosymplectic Yangians based on Gauss decomposition and super-embedding techniques, extending the algebraic framework.

Findings

Derived a Drinfeld-type presentation for ${rak osp}_{N|2m}$ Yangians.

Established a super-version of the embedding theorem.

Identified subalgebras isomorphic to lower-rank Yangians.

Abstract

We use the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the Yangian for the orthosymplectic Lie superalgebra ${\frak osp}_{N|2m}$ to produce its Drinfeld-type presentation. The results rely on a super-version of the embedding theorem which allows one to identify a subalgebra in the $R$-matrix presentation which is isomorphic to the Yangian associated with ${\frak osp}_{N|2m-2}$.