Representations of the modular shifted super Yangian $Y_{1|1}(\sigma )$

Abstract

Let $Y_{1|1}$ be the Yangian associated to the general linear Lie superalgebra ${\mathfrak{gl}}_{1|1}$, defined over an algebraically closed field $\mathbbm{k}$ of characteristic $p>2$. In this paper, we classify the finite dimensional irreducible representations of the restricted super Yangian $Y_{1|1}^{[p]}$ and the restricted truncated shifted super Yangian $Y_{1|1,\ell }^{[p]}(\sigma )$.