Linkage for periplectic supergroups in positive characteristic

Abstract

We consider the periplectic supergroup ${\bf P} (n)$ over a ground field $\Bbbk$ of characteristic $p>2$. We show that there are four blocks of ${\bf P} (n)$ 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.