  We study the Verma modules M(mu(u)) over the Yangian Y(a) associated with a
simple Lie algebra a. We give necessary and sufficient conditions for
irreducibility of M(mu(u)). Moreover, regarding the simple quotient L(mu(u)) of
M(mu(u)) as an a-module, we give necessary and sufficient conditions for
finite-dimensionality of the weight subspaces of L(mu(u)).
