Representations of principal $W$-algebra for the superalgebra $Q(n)$ and the super Yangian $YQ(1)$

Abstract

We classify irreducible representations of finite $W$-algebra of the queer Lie superalgebra $Q(n)$ associated with the principal nilpotent coadjoint orbits. We use this classification and our previous results to obtain a classification of simple finite-dimensional representations of the super Yangian $YQ(1)$.