  We construct by fusion product new irreducible representations of the quantum
affinization $U_q(\hat{sl}_\infty)$. The action is defined via the Drinfeld
coproduct and is related to the crystal structure of semi-standard tableaux of
type $A_\infty$. We call these representations extremal loop weight modules.
The main motivations are applications to quantum toroidal algebras
$U_q(sl_{n+1}^{tor})$: we prove the conjectural link between
$U_q(\hat{sl}_\infty)$ and $U_q(sl_{n+1}^{tor})$ stated in [14] for this family
of representations. We recover in this way the extremal loop weight modules
obtained in [23].
