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

TL;DR

This paper establishes a concrete cyclicity criterion for tensor products of fundamental representations of the Yangian associated with the exceptional Lie algebra G2, demonstrating that all local Weyl modules decompose into ordered tensor products of these fundamental modules.

Contribution

It introduces a specific cyclicity condition for tensor products in the Yangian of G2 and proves that all local Weyl modules are isomorphic to ordered tensor products of fundamental representations.

Findings

Cyclicity condition for tensor products of fundamental representations

Decomposition of local Weyl modules into ordered tensor products

Application to the structure of Yangian modules for G2

Abstract

Let $\mathfrak{g}$ be the exceptional complex simple Lie algebra of type $G_2$. We provide a concrete cyclicity condition for the tensor product of fundamental representations of the Yangian $Y(\mathfrak{g})$. Using this condition, we show that every local Weyl module is isomorphic to an ordered tensor product of fundamental representations of $Y(\mathfrak{g})$.