Principal W-algebras for GL(m|n)

TL;DR

This paper explicitly describes the structure of principal W-algebras for the general linear Lie superalgebra, linking them to shifted Yangians and constructing their irreducible representations.

Contribution

It provides an explicit description of W_{m|n} as a truncation of a shifted Yangian and constructs its irreducible representations.

Findings

W_{m|n} is a truncation of a shifted Yangian

W_{m|n} admits a triangular decomposition

Constructed irreducible representations of W_{m|n}

Abstract

We consider the (finite) $W$-algebra $W_{m|n}$ attached to the principal nilpotent orbit in the general linear Lie superalgebra $\mathfrak{gl}_{m|n}(\mathbb C)$. Our main result gives an explicit description of $W_{m|n}$ as a certain truncation of a shifted version of the Yangian $Y(\mathfrak{gl}_{1|1})$. We also show that $W_{m|n}$ admits a triangular decomposition and construct its irreducible representations.