Modular representations of the Yangian $Y_2$

Let $Y_2$ be the Yangian associated to the general linear Lie algebra ${\mathfrak{g}\mathfrak{l}}_2$, defined over an algebraically closed field $\text{mathbbm}k$ of characteristic $p>0$. In this paper, we study the representation theory of the restricted Yangian $Y_2^{[p]}$. This leads to a description of the representations of ${\mathfrak{g}\mathfrak{l}}_{2n}$, whose $p$-character is nilpotent with Jordan type given by a two-row partition $(n,n)$.