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

Abstract

The minimal irreducible representations of $U_q[gl(m|n)]$, i.e. those irreducible representations that are also irreducible under $U_q[osp(m|n)]$ are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra $U_q[gl(m|n{)}^{(2)}]$. The $U_q[osp(m|n)]$ invariant R-matrices corresponding to the tensor product of any two minimal representations are constructed, thus extending our twisted tensor product graph method to the supersymmetric case. These give new solutions to the spectral-dependent graded Yang-Baxter equation arising from $U_q[gl(m|n{)}^{(2)}]$, which exhibit novel features not previously seen in the untwisted or non-super cases.

19 pages, Latex file

References in corpus (1)

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

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• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
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• Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras
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