Abstract
We investigate the integrable structure of spin chain models with centrally extended
and 
symmetry. These chains have their origin in the planar anti-de Sitter/conformal field
theory correspondence, but they also contain the one-dimensional Hubbard model as a
special case. We begin with an overview of the representation theory of centrally extended
. These results are applied in the construction and investigation of an interesting
S-matrix with symmetry. In particular, they enable a remarkably simple proof
of the Yang–Baxter relation. We also show the equivalence of the
S-matrix to
Shastry's R-matrix and thus uncover a hidden supersymmetry in the integrable structure of the
Hubbard model. We then construct eigenvalues of the corresponding transfer matrix in
order to formulate an analytic Bethe ansatz. Finally, the form of transfer matrix
eigenvalues for models with symmetry is sketched.