Irreducible modules for the quantum affine algebra and its Borel subalgebra

Let Uq(b) denote the standard Borel subalgebra of the quantum affine algebra . We show that the following hold for any choice of scalars 0, 1 from the set 1,−1 : (i) Let V be a finite-dimensional irreducible Uq(b)-module of type ( 0, 1). Then the action of Uq(b) on V extends uniquely to an action of on V. The resulting -module structure on V is irreducible and of type ( 0, 1). (ii) Let V be a finite-dimensional irreducible -module of type ( 0, 1). When the -action is restricted to Uq(b), the resulting Uq(b)-module structure on V is irreducible and of type ( 0, 1).