Quasi-Spin Graded-Fermion Formalism and $gl(m|n)\downarrow osp(m|n)$ Branching Rules

The graded-fermion algebra and quasi-spin formalism are introduced and applied to obtain the $gl(m|n)\downarrow osp(m|n)$ branching rules for the "two-column" tensor irreducible representations of gl(m|n), for the case $m\leq n (n > 2)$. In the case m < n, all such irreducible representations of gl(m|n) are shown to be completely reducible as representations of osp(m|n). This is also shown to be true for the case m=n except for the "spin-singlet" representations which contain an indecomposable representation of osp(m|n) with composition length 3. These branching rules are given in fully explicit form.