Graded limits of simple tensor product of Kirillov-Reshetikhin modules for $U_q(\tilde{\mathfrak {sl}}_{n+1})$

TL;DR

This paper investigates the graded limits of tensor products of Kirillov-Reshetikhin modules for quantum affine algebra, showing they correspond to fusion products and providing explicit defining relations.

Contribution

It establishes that graded limits of tensor products are isomorphic to fusion products and derives defining relations using recent results.

Findings

Graded limits are isomorphic to fusion products.

Explicit defining relations for graded limits are provided.

The results connect tensor product modules with fusion product structures.

Abstract

We study the graded limits of simple $U_q(\tilde{\mathfrak{sl}}_{n+1})$-modules which are isomorphic to tensor products of Kirillov-Reshetikhin modules associated to a fix fundamental weight. We prove that every such module admits a graded limit which is isomorphic to the fusion product of the graded limits of its tensor factors. Moreover, using recent results of Naoi, we exhibit a set of defining relations for these graded limits.