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

Abstract

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 $m\le n(n>2)$. 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.

19 pages, Latex file

References in corpus (2)

• On the solution of a supersymmetric model of correlated electrons
• The long delayed solution of the Bukhvostov Lipatov model

Cited by in corpus (1)

• Twisted Quantum Affine Superalgebra $U_q[gl(m|n{)}^{(2)}]$ and New $U_q[osp(m|n)]$ Invariant R-matrices