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

## TL;DR

This paper classifies irreducible representations of the finite W-algebra for the queer Lie superalgebra Q(n) and uses this to classify simple finite-dimensional representations of the super Yangian YQ(1).

## Contribution

It provides the first complete classification of irreducible representations for these algebraic structures, linking W-algebras and super Yangians.

## Key findings

- Classified irreducible representations of finite W-algebra for Q(n).
- Derived classification of simple finite-dimensional representations of YQ(1).
- Established connections between W-algebras and super Yangians.

## 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 $YQ(1)$.