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

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

1999-05-04

arxiv.org/abs/math-ph/9905002v1

J. Math. Phys. 40 (1999) 5371-5386

Physics

Mathematical Physics

19 pages, Latex file

Scientific paper

10.1063/1.533075

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.

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