Cyclicity and R-matrices

TL;DR

This paper proves that if pairwise tensor products of certain modules are cyclic, then their full tensor product is cyclic, using R-matrix analysis in quantum affine algebra representations.

Contribution

It establishes a new criterion for cyclicity of tensor products of modules based on pairwise cyclicity, advancing understanding of module structures in quantum affine algebras.

Findings

Pairwise cyclic tensor products imply full tensor product cyclicity

Analysis of R-matrices underpins the main proof

Provides new insights into module tensor product structures

Abstract

Let $S_1, \cdots, S_N$ simple finite-dimensional modules of a quantum affine algebra. We prove that if $S_i\otimes S_j$ is cyclic for any $i < j$ (i.e. generated by the tensor product of the highest weight vectors), then $S_1\otimes \cdots \otimes S_N$ is cyclic. The proof is based on the study of $R$-matrices.