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

The graded-fermion algebra and quasi-spin formalism are introduced and applied to obtain the gl(m|n) ↓ osp(m|n) branching rules for the “two-column” tensor irreducible representations of gl(m|n), for the case m ≤ 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. Gould and Zhang: gl(m|n) ↓ osp(m|n) Branching Rules 1