Small representations of quantum affine algebras

We characterize the finite-dimensional representations of the quantum affine algebra U_q(_n+1) (whereq ^× is not a root of unity) which are irreducible as representations of U_q(sl_n+1). We call such representations small. In 1986, Jimbo defined a family of homomorphismsev_afrom U_q(sl_n+1) to (an enlargement of) U_q(sl_,n+1), depending on a parametera ^·. A second family,ev^acan be obtained by a small modification of Jimbo's formulas. We show that every small representation of U_q(_n+1) is obtained by pulling back an irreducible representation of U_q(sl_n+1) byev_aorev^afor somea ^·.