Kac-Wakimoto conjecture for the periplectic Lie superalgebra

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.

Preliminary version. arXiv admin note: text overlap with arXiv:1807.09478