Graded Limits of Simple Tensor Product of Kirillov–Reshetikhin Modules for

Abstract

We study graded limits of simple U q n+1 -modules which are isomorphic to tensor products of Kirillov-Reshetikhin modules associated to a fixed 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.

Tensor Products of Kirillov–Reshetikhin Modules and Fusion Products

“…• In the case where ℓ 1 = · · · = ℓ p = 1, the result follows from [CL06,FL07,Nao12b]. • In the case of type A with i 1 = · · · = i p and a 1 = · · · = a p , the result is proved in [BP15]. • For a special class of tensor products appearing in the T -system, the result follows from [CV15].…”

On Tensor Products of a Minimal Affinization With an Extreme Kirillov-Reshetikhin Module for Type A

“…It would then be interesting to eventually study the results of the present paper from the perspective of T -systems and cluster algebras. The connection of graded limits of tensor products of finite-dimensional representations of quantum affine algebras with the notion of fusion products in the sense of [12] is also another topic of recent interest (see for instance [1,2,26,27] and references therein). Thus, it should also be interesting to study the graded limits of the tensor products studied here in that context as well.…”