  In this paper, we study the representations of the periplectic Lie
superalgebra using the Duflo-Serganova functor. Given a simple
$\mathfrak{p}(n)$-module $L$ and a certain element $x\in \mathfrak{p}(n)$ of
rank $1$, we give an explicit description of the composition factors of the
$\mathfrak{p}(n-1)$-module $DS_x(L)$, which is defined as the homology of the
complex $$\Pi M \xrightarrow{x} M \xrightarrow{x} \Pi M.$$ In particular, we
show that this $\mathfrak{p}(n-1)$-module is multiplicity-free. We then use
this result to give a simple explicit combinatorial formula for the
superdimension of a simple integrable finite-dimensional
$\mathfrak{p}(n)$-module, based on its highest weight. In particular, this
reproves the Kac-Wakimoto conjecture for $\mathfrak{p}(n)$, which was proved
earlier by the authors.
