On shifted super Yangians and a class of finite W-superalgebras

TL;DR

This paper establishes a connection between finite W-superalgebras associated with nilpotent elements in general linear Lie superalgebras and shifted super Yangians, providing a new realization under specific conditions.

Contribution

It introduces a realization of finite W-superalgebras as quotients of shifted super Yangians for certain Jordan types, advancing the understanding of their structure.

Findings

Realization of W-superalgebras as quotients of shifted super Yangians

Conditions on Jordan type for the realization to hold

Enhanced understanding of the algebraic structure of W-superalgebras

Abstract

We study the finite W-superalgebra $W_e$ associated to a nilpotent element $e$ in a general linear Lie superalgebra. Under certain restriction on the Jordan type of $e$, we give a realization of $W_e$ in terms of a quotient of a shifted super Yangian.