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

P. Kondratowicz; P. Podles

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arXiv · hep-th/9405079

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

P. Kondratowicz·P. Podles

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Abstract

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.

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P. Kondratowicz, P. Podles. 1996-01-21. On representation theory of quantum $SL_q(2)$ groups at roots of unity. https://arxiv.org/abs/hep-th/9405079

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