Simple tensor products

TL;DR

This paper characterizes when tensor products of simple objects in the category of finite-dimensional quantum affine algebra representations are simple, showing it suffices to check pairwise tensor products for simplicity.

Contribution

It provides a necessary and sufficient condition for the simplicity of tensor products of simple objects in quantum affine algebra representations.

Findings

Tensor product of simple objects is simple iff all pairwise tensor products are simple.

Simplifies the analysis of tensor products in quantum affine algebra representations.

Provides a criterion for understanding the structure of tensor products in the category F.

Abstract

Let F be the category of finite dimensional representations of an arbitrary quantum affine algebra. We prove that a tensor product $S_1\otimes ... \otimes S_N$ of simple objects of F is simple if and only if for any $i < j$, $S_i\otimes S_j$ is simple.