Local Weyl modules and cyclicity of tensor products for Yangians

Abstract

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).