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

• Autorzy: Piotr Kondratowicz , Piotr Podleś
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 40
• Numer: 1
• Strony: 223-248

Daty

wydano

1997

Twórcy

autor

Piotr Kondratowicz

• Department of Mathematical Methods in Physics, University of Warsaw , Hoża 74, 00-682 Warszawa, Poland

autor

Piotr Podleś

• Department of Mathematical Methods in Physics, University of Warsaw , Hoża 74, 00-682 Warszawa, Poland

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