  In this paper we construct all the primitive idempotents of the restricted
quantum group $\overline{U}_q (sl_2)$ and also determine the multiplication
rules among a basis given by the action of generators of $\bar{U}_q (sl_2)$ to
the idempotents. By using this result we construct a basis of the space of
symmetric linear functions of $\overline{U}_q (sl_2)$ and determine the
decomposition of the integral of the dual of $\overline{U}_q (sl_2)$ twisted by
the balancing element to the basis of the space of symmetric linear functions.
