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

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.Comment: 19 pages, Latex fil

Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups

We introduce the quasi-Hopf superalgebras which are $Z_2$ graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymmetric case. Two types of elliptic quantum supergroups are defined, that is the face type $B_{q,\lambda}(G)$ and the vertex type $A_{q,p}[\hat{sl(n|n)}]$ (and $A_{q,p}[\hat{gl(n|n)}]$), where $G$ is any Kac-Moody superalgebra with symmetrizable generalized Cartan matrix. It appears that the vertex type twistor can be constructed only for $U_q[\hat{sl(n|n)}]$ in a non-standard system of simple roots, all of which are fermionic.Comment: 22 pages, Latex fil