Modular representations of the Yangian Y 2 $Y_2$

Abstract

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