  We define integrable representations of quantum toroidal algebras of type A
by tensor product, using the Drinfeld "coproduct". This allow us to recover the
vector representations recently introduced by Feigin-Jimbo-Miwa-Mukhin [6] and
constructed by the author [21] as a subfamily of extremal loop weight modules.
In addition we get new extremal loop weight modules as subquotients of tensor
powers of vector representations. As an application we obtain
finite-dimensional representations of quantum toroidal algebras by specializing
the quantum parameter at roots of unity.
