# On the finite $W$-algebra for the Lie superalgebra Q(N) in the non-regular case

## TL;DR

This paper investigates the structure of finite W-algebras associated with the queer Lie superalgebra Q(n) in non-regular cases, establishing an isomorphism with a quotient of the super-Yangian of Q(n/l).

## Contribution

It provides a new isomorphism result connecting finite W-algebras for Q(n) with super-Yangians in non-regular cases, expanding understanding of their algebraic structure.

## Key findings

- Finite W-algebra for Q(n) is isomorphic to a quotient of the super-Yangian of Q(n/l).
- The result applies to non-regular nilpotent orbits with Jordan blocks of size l.
- The paper extends the theory of W-algebras in the context of Lie superalgebras.

## Abstract

In this paper we study the finite W-algebra for the queer Lie superalgebra Q(n) associated with the non-regular even nilpotent coadjoint orbits in the case when the corresponding nilpotent element has Jordan blocks each of size l. We prove that this finite W-algebra is isomorphic to a quotient of the super-Yangian of Q({n/l})