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On representation theory of quantum \(SL_ q(2)\) groups at roots of unity. (English) Zbl 0890.17017

Budzyński, Robert (ed.) et al., Quantum groups and quantum spaces. Lectures delivered during the minisemester, Warsaw, Poland, December 1, 1995. Warszawa: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 40, 223-248 (1997).
The authors classify the irreducible representations of the quantum group \(SL_q(2)\), \(q\) a root of unity. The result was known for odd roots of unity from B. Parshall and J. Wang. An example of a representation which is not completely reducible is constructed, and it is proved that \(SL_q(2)\) does not have a Haar functional. The representations of the quantum enveloping algebra \(U_q(sl(2))\) corresponding to the irreducible representations of \(SL_q(2)\) are described.
For the entire collection see [Zbl 0865.00041].

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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