7 research outputs found

    Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]

    Full text link
    Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal RR-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation π\pi, which acts on the vector module VV, to one side of a universal RR-matrix gives a Lax operator. In this paper a Lax operator is constructed for the CC-type quantum superalgebras Uq[osp(2n)]U_q[osp(2|n)]. This can in turn be used to find a solution to the Yang-Baxter equation acting on VVWV \otimes V \otimes W where WW is an arbitrary Uq[osp(2n)]U_q[osp(2|n)] module. The case W=VW=V is included here as an example.Comment: 15 page

    Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras

    Full text link
    The Perk--Schultz model may be expressed in terms of the solution of the Yang--Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra Uq[sl(mn)]U_q[sl(m|n)], with a multiparametric co-product action as given by Reshetikhin. Here we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras Uq[osp(mn)]U_q[osp(m|n)]. In this manner we obtain generalisations of the Perk--Schultz model.Comment: 10 pages, 2 figure

    Eigenvalues of Casimir invariants for Uq[osp(m|n)]

    Get PDF
    For each quantum superalgebra U-q[osp(m parallel to n)] with m > 2, an infinite family of Casimir invariants is constructed. This is achieved by using an explicit form for the Lax operator. The eigenvalue of each Casimir invariant on an arbitrary irreducible highest weight module is also calculated. (c) 2005 American Institute of Physics

    Lax operator for the quantised orthosymplectic superalgebra Uq[osp(m\n)]

    No full text
    Representations of quantum superalgebras provide a natural framework in which to model supersymmetric quantum systems. Each quantum superalgebra, belonging to the class of quasi-triangular Hopf superalgebras, contains a universal R-matrix which automatically satisfies the Yang-Baxter equation. Applying the vector representation pi, which acts on the vector module V, to the left-hand side of a universal R-matrix gives a Lax operator. In this article a Lax operator is constructed for the quantised orthosymplectic superalgebras U (q) [osp(m|n)] for all m > 2, n >= 0 where n is even. This can then be used to find a solution to the Yang-Baxter equation acting on V circle times V circle times W, where W is an arbitrary U (q) [osp(m|n)] module. The case W = V is studied as an example
    corecore