Representations of the Yangians associated with Lie superalgebras ${\frak{osp}}(1|2n)$

TL;DR

This paper classifies finite-dimensional irreducible representations of Yangians linked to orthosymplectic Lie superalgebras ${\frak{osp}}_{1|2n}$ using Drinfeld polynomials, building on previous work for the case $n=1$.

Contribution

It provides a complete classification of these representations for all $n$, extending earlier results for the case $n=1$.

Findings

Classification of representations via Drinfeld polynomials

Extension of previous $n=1$ results to general $n$

Framework for understanding Yangian representations of ${\frak{osp}}_{1|2n}$

Abstract

We classify the finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak{osp}}_{1|2n}$ in terms of the Drinfeld polynomials. The arguments rely on the description of the representations in the particular case $n=1$ obtained in our previous work.