7 research outputs found

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

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

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

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
$U_q[sl(m|n)]$, 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 $U_q[osp(m|n)]$. 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)]

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)]

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