Twisted quantum affine superalgebra Uq[gl(m|n)(2)] and new Uq[osp(m|n)] invariant R-matrices Original Research Article

The minimal irreducible representations of Uq[gl(m|n)], i.e. those irreducible representations that are also irreducible under Uq[osp(m|n)] are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra Uq[gl(m|n)(2)]. The Uq[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 Uq[gl(m|n)(2)], which exhibit novel features not previously seen in the untwisted or non-super cases.