  Irreducible representations of quantum groups $SL_q(2)$ (in Woronowicz'
approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the~case of
$q$ being an~odd root of unity. Here we find the~irreducible representations
for all roots of unity (also of an~even degree), as well as describe
"the~diagonal part" of tensor product of any two irreducible representations.
An~example of not completely reducible representation is given. Non--existence
of Haar functional is proved. The~corresponding representations of universal
enveloping algebras of Jimbo and Lusztig are provided. We also recall the~case
of general~$q$. Our computations are done in explicit way.
