On representation theory of quantum $SL_q(2)$ groups at roots of unity
| dc.creator | Kondratowicz, P. | |
| dc.creator | Podles, P. | |
| dc.date | 1994-05-12 | |
| dc.date | 1996-01-21 | |
| dc.date.accessioned | 2026-07-07T09:03:39Z | |
| dc.date.available | 2026-07-07T09:03:39Z | |
| dc.description | 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. | |
| dc.description | 31 pages, Section 2.7 added and other minor changes | |
| dc.identifier | https://arxiv.org/abs/hep-th/9405079 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9405079 | |
| dc.identifier | Banach Center Publ. 40 (1997) 223-248 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149093 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | On representation theory of quantum $SL_q(2)$ groups at roots of unity | |
| dc.type | text |