On representation theory of quantum SLq(2) groups at roots of unity

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Irreducible representations of quantum groups SLq(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.