Matrix difference equations and a nested Bethe ansatz

The system of SU(N)- and U(N)-matrix difference equations are solved by means of a nested version of a generalized Bethe ansatz, also the called 'off shell' Bethe ansatz (Babujian H M 1990 Correlation functions in WZNW model as a Bethe wavefunction for the Gaudin magnets Proc. XXIVth Int. Symp. (Ahrenshoop, Zeuthen)). To solve this new Bethe ansatz in the algebraic language analogous to the conventional case, a new type of monodromy matrices is introduced. They fulfil a new type of Yang-Baxter equations which simplify the proofs. Using a similar approach as for the conventional nested Bethe ansatz the problem is solved iteratively. The vanishing of the 'unwanted terms' of the first level ansatz is equivalent to a set of second level difference equations. The solutions are obtained as sums over 'off-shell' Bethe vectors. These sums are 'Jackson-type integrals'. The highest weight property of the solutions is proved. The solutions are calculated explicitly for several examples of SU(N)- and U(N)-representations.