  Let $G=GL(m|n)$ be a general linear supergroup and $G_{ev}$ be its even
subsupergroup isomorphic to $GL(m)\times GL(n)$. In this paper we use the
explicit description of $G_{ev}$-primitive vectors in the costandard
supermodule $\nabla(\lambda)$, the largest polynomial $G$-subsupermodule of the
induced supermodule $H^0_G(\lambda)$, for $(m|n)$-hook partition $\lambda$, and
a properties of certain morphisms $\psi_k$ to derive results related to the odd
linkage for $G$ over a field $F$ of characteristic different from $2$.
