ANALYTIC BETHE-ANSATZ FOR FUNDAMENTAL REPRESENTATIONS OF YANGIANS

We study the analytic Bethe ansatz in solvable vertex models associated with the Yangian Y(X(r)) or its quantum affine analogue U-q(X(r)((1)))) for X(r) = B-r C-r and D-r. Eigenvalue formulas are proposed for the transfer matrices related to all the fundamental representations of Y(X(r)). Under the Bethe ansatz equation, we explicitly prove that they are pole-free, a crucial property in the ansatz. Conjectures are also given on higher representation cases by applying the T-system, the transfer matrix functional relations proposed recently. The eigenvalues are neatly described in terms of Yangian analogues of the semi-standard Young tableaux.