Unitary Representations of Noncompact Quantum Groups at Roots of Unity

Details Unitary Representations of Noncompact Quantum Groups at Roots of Unity Unitary Representations of Noncompact Quantum Groups at Roots of Unity

1999-07-05

arxiv.org/abs/math/9907021v2

Rev.Math.Phys. 13 (2001) 1035

Mathematics

Quantum Algebra

23 pages, LaTeX. Typos corrected and some explanations added. To appear in Rev. Math. Phys

Scientific paper

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.

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