In this note we consider the algebra $U_q(\hat{sl}_\infty)$ and we study the
category O of its integrable representations. The main motivations are
applications to quantum toroidal algebras. In this context, we state a general
positivity conjecture for representations of $U_q(\hat{sl}_\infty)$ viewed as
representations of quantum toroidal algebras, that we prove for
Kirillov-Reshetikhin modules.