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Unitary Representations of Noncompact Quantum Groups at Roots of Unity | | Harold Steinacker
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5 Jul 1999 | | Journal: | Rev.Math.Phys. 13 (2001) 1035 | | Subject: | Quantum Algebra; Representation Theory | math.QA hep-th math.RT | | Abstract: | Noncompact forms of the Drinfeld-Jimbo quantum groups U_q(g) with (H_i)* = H_i, (X_i^{+-})* = s_i X_i^{-+} for s_i= +-1 are studied at roots of unity. This covers g = so(n,2p), su(n,p), so*(2l), sp(n,p), sp(l,R), and exceptional cases. Finite-dimensional unitary representations are found for all these forms, for even roots of unity. Their classical symmetry induced by the Frobenius-map is determined, and the meaning of the extra quasi-classical generators appearing at even roots of unity is clarified. The unitary highest weight modules of the classical case are recovered in the limit q -> 1. | | Source: | arXiv, math.QA/9907021 | | Services: | Forum | Review | PDF | Favorites | |
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