Linkage for periplectic supergroups in positive characteristic

Abstract

We consider the periplectic supergroup $\mathbf{P}(n)$ over a ground field $\mathbb{k}$ of characteristic $p>2$. We show that there are four blocks of $\mathbf{P}(n)$ of simple supermodules $L^{\epsilon }(\lambda )$ corresponding to dominant weights $\lambda$ of even and odd lengths, and the even and odd parity $\epsilon$ of their highest weight vector.