A Clebsch-Gordan decomposition in positive characteristic

Let K be an algebraically closed field and G=SL2(K). Let E be the natural module and SrE the rth symmetric power. We consider here, for r,s≥0, the tensor product of SrE and the dual of SsE. In characteristic zero this tensor product decomposes according to the Clebsch-Gordan formula. We consider here the situation when K is a field of positive characteristic. We show that each indecomposable component occurs with multiplicity one and identify which modules occur for given r and s.