Tensor Product of the Fundamental Representations for the Quantum Loop Algebras of Type A at Roots of Unity

TL;DR

This paper investigates the conditions under which tensor products of fundamental representations for restricted quantum loop algebras of type A at roots of unity remain irreducible, providing a comprehensive characterization.

Contribution

It establishes necessary and sufficient conditions for irreducibility of tensor products in this specific quantum algebra setting.

Findings

Derived explicit criteria for irreducibility

Characterized tensor product behavior at roots of unity

Enhanced understanding of quantum loop algebra representations

Abstract

In this paper, we consider the necessary and sufficient conditions for the tensor product of the fundamental representations for the restricted quantum loop algebras of type A at roots of unity to be irreducible.