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

Abstract

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.

15 pages

References in corpus (4)

• R-matrices and Spectrum of Vertex Models based on Superalgebras
• New R-matrices from Representations of Braid-Monoid Algebras based on Superalgebras
• Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras
• Eigenvalues of Casimir invariants for Uq[osp(m|n)]

Cited by in corpus (1)

• Exact solution and finite size properties of the $U_q[osp(2|2m)]$ vertex model