Analytic Bethe Ansatz for Fundamental Representations of Yangians*

We study the analytic Bethe ansatz in solvable vertex models associated with the Yangian Y (Xr) or its quantum affine analogue Uq(X (1) r ) for Xr = Br, Cr and Dr. Eigenvalue formulas are proposed for the transfer matrices related to all the fundamental representations of Y (Xr). 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 semistandard Young tableaux. * Short title: Analytic Bethe ansatz † E-mail: [email protected] ‡ E-mail: [email protected]