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On representation theory of quantum $SL_{q}(2)$ groups at roots of unity

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Kondratowicz P., Podleś P.

Banach Center Publications

1997

tom 40

nr 1

223-248

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 the tensor product of any two irreducible representations. An example of a 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.

Ograniczanie wyników

1 Banach Center Publications

1 Kondratowicz P.

1 Podleś P.

1 1997

Wyniki wyszukiwania

On representation theory of quantum $SL_{q}(2)$ groups at roots of unity