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

TL;DR

This paper introduces a graded-fermion algebra and quasi-spin formalism to derive explicit branching rules for tensor irreducible representations of gl(m|n) when restricted to osp(m|n), revealing complete reducibility except for certain spin-singlet cases.

Contribution

It provides the first explicit derivation of gl(m|n) to osp(m|n) branching rules for two-column tensor irreducible representations using a novel formalism.

Findings

All irreducible representations are completely reducible when m < n.

For m = n, spin-singlet representations contain indecomposable osp(m|n) components.

Explicit formulas for the branching rules are provided.

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