Local Weyl modules and cyclicity of tensor products for Yangians

Abstract

We provide a sufficient condition for the cyclicity of an ordered tensor product $L=V_{a_1}({\omega }_{b_1})\otimes V_{a_2}({\omega }_{b_2})\otimes ...\otimes V_{a_k}({\omega }_{b_k})$ of fundamental representations of the Yangian $Y(\mathfrak{g})$. When $\mathfrak{g}$ 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 $\mathfrak{g}={\mathfrak{sl}}_{l+1}$, 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 $Y(\mathfrak{g})$. We show that every local Weyl module is isomorphic to an ordered tensor product of fundamental representations of $Y(\mathfrak{g})$.

26 page

References in corpus (1)

• Finite-dimensional Representations of Yangians

Cited by in corpus (1)

• Local Weyl modules and cyclicity of tensor products for Yangians of $G_2$