Linkage principle for ortho-symplectic supergroups

The purpose of the paper is to derive linkage principle for modular representations of ortho-symplectic supergroups. We follow the approach of Doty and investigate in detail the representation theory of the orthosymplectic group $OSP(2\mathrm{\mid }1)$ and that of its Frobenius thickening. Using the description of flags and adjacent Borel supersubgroups we derive first the strong linkage for the Frobenius thickening $G_{r}T$ of the orthosymplectic supergroup $G$ of type $SpO(2m\mathrm{\mid }2n+1)$ and $SpO(2m\mathrm{\mid }2n)$. Based on this, we derive the linkage principle for orthosymplectic supergroup $SpO(2m\mathrm{\mid }2n+1)$ and $SpO(2m\mathrm{\mid }2n)$.