Tensor products of Kirillov-Reshetikhin modules and fusion products

TL;DR

This paper investigates the classical limits of tensor products of Kirillov-Reshetikhin modules over quantum loop algebras, demonstrating their realization via fusion products and providing defining relations for these limits.

Contribution

It introduces a new understanding of classical limits of tensor products of Kirillov-Reshetikhin modules using fusion products and establishes their defining relations.

Findings

Classical limits of tensor products are realized through fusion products.

Defined relations for the fusion product of classical limits.

Enhanced understanding of module structures in quantum loop algebras.

Abstract

We study the classical limit of a tensor product of Kirillov-Reshetikhin modules over a quantum loop algebra, and show that it is realized from the classical limits of the tensor factors using the notion of fusion products. In the process of the proof, we also give defining relations of the fusion product of the (graded) classical limits of Kirillov-Reshetikhin modules.