Yang–Baxter algebra for the n-harmonic oscillator realisation of Sp(2n,R)

Using a rational R-matrix associated with the 4×4 defining matrix representation of c2≅sp(4), the Lie algebra of Sp(4), a one-site operator solution of the associated Yang–Baxter algebra acting in the Fock space of two harmonic oscillators is derived. This is used to define N-site integrable systems, which are soluble by a version of the algebraic Bethe ansatz method without nesting. All essential aspects of the work generalise directly from c2 to cn.