On the one-dimensional representations of finite W-superalgebras for 𝔤𝔩M|N

Let [Formula: see text] be the general linear Lie superalgebra over an algebraically closed field [Formula: see text] of characteristic zero. Fix an arbitrary even nilpotent element [Formula: see text] in [Formula: see text] and let [Formula: see text] be the finite [Formula: see text]-superalgebra associated to the pair [Formula: see text]. In this paper, we will give a complete classification of one-dimensional representations for [Formula: see text]. To achieve this, we use the tool of shifted super Yangians to determine the commutative quotients of the finite [Formula: see text]-superalgebras.