Quasispin graded-fermion formalism and gl(m vertical bar n)down arrow osp(m vertical bar n) branching rules

The graded-fermion algebra and quasispin formalism are introduced and appli ed to obtain the gl(m\n)down arrow osp(m\n) branching rules for the "two- c olumn" tensor irreducible representations of gl(m\n), for the case m less t han or equal to n(n > 2). In the case m < n, all such irreducible represent ations of gl(m\n) are shown to be completely reducible as representations o f 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 representat ion of osp(m\n) with composition length 3. These branching rules are given in fully explicit form. (C) 1999 American Institute of Physics. [S0022-2488 (99)04410-2].