On periodic representations of quantum groups

Journal Article · Mon Jun 01 04:00:00 EDT 1992 · International Journal of Modern Physics B; (United States)

DOI:https://doi.org/10.1142/S0217979292000918· OSTI ID:7173032

Aarnaudon, D ^[1]

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1. Center de Physique Theorique de l'Ecole Polytechnique, 91128 Palaiseau Cedex (FR)

In this paper the authors present some results on representations of quantum groups at the root of unity. In the case of SL(2){sub q}, the classification of the finite dimensional irreducible representations is given. For U{sub q}(G) with G a semi-simple or affine Lie algebra and q an mth root of unity (m odd), we classify the representations of dimension m{sup rankG} on which the actions of the Chevalley generators are injective. Finally, the authors adapt the Gelfand-Zetlin basis to the case of SL(N){sub q} and IU(N){sub q}.

• OSTI ID: 7173032
• Journal Information: International Journal of Modern Physics B; (United States), Journal Name: International Journal of Modern Physics B; (United States) Vol. 6:11-12; ISSN 0217-9792; ISSN IJPBE
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
662110 -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CLASSIFICATION
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MECHANICS
QUANTUM MECHANICS
SL GROUPS
SYMMETRY GROUPS