# Representations of Super $W(2,2)$ algebra $\mathfrak{L}$

## TL;DR

This paper investigates the representation theory of the super W(2,2) algebra, classifying its irreducible modules, analyzing conjugate-linear anti-involutions, and identifying unitary modules of intermediate series.

## Contribution

It provides the first classification of irreducible modules of intermediate series and characterizes unitary modules for the super W(2,2) algebra.

## Key findings

- No mixed irreducible modules exist for ${rak{L}}$
- Complete classification of irreducible modules of intermediate series
- Determination of conjugate-linear anti-involution and unitary modules

## Abstract

In paper, we study the representation theory of super $W(2,2)$ algebra ${\mathfrak{L}}$. We prove that ${\mathfrak{L}}$ has no mixed irreducible modules and give the classification of irreducible modules of intermediate series. We determinate the conjugate-linear anti-involution of ${\mathfrak{L}}$ and give the unitary modules of intermediate series.