Local Weyl modules and cyclicity of tensor products for Yangians

We provide a sufficient condition for the cyclicity of an ordered tensor product L = Va1(ωb1) ⊗ Va2(ωb2) ⊗ . . . ⊗ Vak(ωbk) of fundamental representations of the Yangian Y (g). When g is a classical simple Lie algebra, we make the cyclicity condition concrete, which leads to an irreducibility criterion for the ordered tensor product L. In the case when g = sll+1, a sufficient and necessary condition for the irreducibility of the ordered tensor product L is obtained. The cyclicity of the ordered tensor product L is closely related to the structure of the local Weyl modules of Y (g). We show that every local Weyl module is isomorphic to an ordered tensor product of fundamental representations of Y (g).