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 $Y(\mathfrak{g})$.

arXiv comment26 page

References in corpus (8)

• Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras
• Multi-dimensional Weyl Modules and Symmetric Functions
• The restricted Kirillov-Reshetikhin modules for the current and twisted current algebras
• Yangians, Integrable Quantum Systems and Dorey's rule
• Finite-dimensional irreducible representations of twisted Yangians
• Irreducible representations of Yangians
• Fusion, mass, and representation theory of the Yangian algebra
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Cited by in corpus (8)

• Equivalences between three presentations of orthogonal and symplectic Yangians
• Asymptotic Representations of Quantum Affine Superalgebras
• Fundamental representations of quantum affine superalgebras and R-matrices
• Poles of finite-dimensional representations of Yangians
• Yangians and Baxter's relations
• Braid group actions and tensor products for Yangians
• Braid group actions, Baxter polynomials, and affine quantum groups
• Local Weyl modules and cyclicity of tensor products for Yangians of $G_2$