# Kac-Wakimoto conjecture for the periplectic Lie superalgebra

## TL;DR

This paper proves the Kac-Wakimoto conjecture for the periplectic Lie superalgebra, establishing that simple modules in non-maximal atypicality blocks have zero superdimension, advancing understanding of superalgebra representation theory.

## Contribution

The paper provides a proof of the Kac-Wakimoto conjecture specifically for the periplectic Lie superalgebra, a case previously unresolved.

## Key findings

- Simple modules in non-maximal atypicality blocks have superdimension zero
- The conjecture holds for the periplectic Lie superalgebra
- Advances the classification of modules in superalgebra theory

## Abstract

We prove the Kac-Wakimoto conjecture for the periplectic Lie superalgebra $\mathfrak{p}(n)$, stating that any simple module lying in a block of non-maximal atypicality has superdimension zero.