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

TL;DR

This paper classifies finite dimensional irreducible representations of certain restricted super Yangians related to the Lie superalgebra gl_{1|1}, extending understanding of their structure over fields of characteristic p>2.

Contribution

It provides a classification of irreducible representations for restricted super Yangians and their shifted variants, a novel result in the representation theory of superalgebras.

Findings

Classification of finite dimensional irreducible representations of Y_{1|1}^{[p]}

Classification of irreducible representations of Y_{1|1, ext{ell}}^{[p]}(\sigma)

Extension of representation theory to super Yangians in characteristic p>2

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 $Y_{1|1,\ell}^{[p]}(\sigma)$.