Principal W-algebras for GL(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.