Centre and representations of small quantum superalgebras at roots of unity |
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Authors: | D. Arnaudon M. Bauer |
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Affiliation: | (1) Chemin de Bellevue, BP 110, 74941 Annecy-le-Vieux Cedex, France;(2) Service de Physique Théorique, C.E.A. Saclay, F-91191 Gif-sur-Yvette, France;(3) URA 1436 du CNRS, Associée à l'E.N.S. de Lyon et à l'Université de Savoie, France |
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Abstract: | When the deformation parameter is a root of unity, the centre of a quantum group can be described by a set of generators and non trivial relations. In the case ofUq(sl(N)), these relations simply derive from the expressions of the deformed Casimir operators. In the case ofUq(osp(1|2)), the relation is simple if we use an operator which anticommutes with the fermionic generators and whose square is the quadratic Casimir. This operator also simplifies the classification of finite dimensional irreducible representations. In the case ofUq(sl(1|2)), the relations derive from the (infinite set of) standard Casimir operators.Presented at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–22 June 1996. |
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