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

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

1994-05-12

arxiv.org/abs/hep-th/9405079v3

Banach Center Publ. 40 (1997) 223-248

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, Section 2.7 added and other minor changes

Scientific paper

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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