  Let $U_q(\hat{sl}_2)^{\geq 0}$ denote the Borel subalgebra of the quantum
affine algebra $U_q(\hat{sl}_2)$. We show that the following hold for any
choice of scalars $\epsilon_0, \epsilon_1$ from the set ${1,-1}$.
  (i) Let $V$ be a finite-dimensional irreducible $U_q(\hat{sl}_2)^{\geq
0}$-module of type $(\epsilon_0,\epsilon_1)$. Then the action of
$U_q(\hat{sl}_2)^{\geq 0}$ on $V$ extends uniquely to an action of
$U_q(\hat{sl}_2)$ on $V$. The resulting $U_q(\hat{sl}_2)$-module structure on
$V$ is irreducible and of type $(\epsilon_0,\epsilon_1)$.
  (ii) Let $V$ be a finite-dimensional irreducible $U_q(\hat{sl}_2)$-module of
type $(\epsilon_0,\epsilon_1)$. When the $U_q(\hat{sl}_2)$-action is restricted
to $U_q(\hat{sl}_2)^{\geq 0}$, the resulting $U_q(\hat{sl}_2)^{\geq 0}$-module
structure on $V$ is irreducible and of type $(\epsilon_0,\epsilon_1)$.
