# Non-standard Verma type modules for $\mathfrak{q}(n)^{(2)}$

## TL;DR

This paper investigates non-standard Verma modules over the Kac-Moody queer Lie superalgebra rak{q}(n)^{(2)}, providing conditions for irreducibility and classifying certain irreducible modules within related Heisenberg superalgebras.

## Contribution

It introduces new criteria for irreducibility of non-standard Verma modules and classifies irreducible diagonal b-graded modules over specific Heisenberg superalgebras.

## Key findings

- Identified sufficient conditions for module irreducibility.
- Classified all irreducible diagonal b-graded modules in certain superalgebras.
- Extended understanding of module structures over rak{q}(n)^{(2)}.

## Abstract

We study non-standard Verma type modules over the Kac-Moody queer Lie superalgebra $\mathfrak{q}(n)^{(2)}$. We give a sufficient condition under which such modules are irreducible. We also give a classification of all irreducible diagonal $\mathbb{Z}$-graded modules over certain Heisenberg Lie superalgebras contained in $\mathfrak{q}(n)^{(2)}$.