A construction of symmetric linear functions of the restricted quantum group \overline{U}_q (sl_2)

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.