Solvable gaudin models for higher rank symplectic algebras

We study generalisations of theXXX-model to higher rank underlying symplectic algebras in the semi-classical approximation. With the help of the metaplectic representation ofsp(2n,ℝ) we establish general results that are useful in the analysis of these algebras, and hence solve the algebraic Bethe ansatz explicitly in this representation. Thesu(n) multiplet structure of the Bethe eigenstates is revealed. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. This work was partly supported by PPARC.