Polynomial Relations in the Centre of U_q(sl(N))

Daniel Arnaudon; Michel Bauer

doi:10.1007/bf00805857

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arXiv · hep-th/9310030

Polynomial Relations in the Centre of U_q(sl(N))

Daniel Arnaudon·Michel Bauer

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Abstract

When the parameter of deformation q is a m-th root of unity, the centre of U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new generators, which are basically the m-th powers of all the Cartan generators of U_q(sl(N)). All these central elements are however not independent. In this letter, generalising the well-known case of U_q(sl(2)), we explicitly write polynomial relations satisfied by the generators of the centre. Application to the parametrization of irreducible representations and to fusion rules are sketched.

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Daniel Arnaudon, Michel Bauer. 1993-10-06. Polynomial Relations in the Centre of U_q(sl(N)). https://doi.org/10.1007/bf00805857

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