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

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

1993-10-06

arxiv.org/abs/hep-th/9310030v1

Letters in Math. Physics 30 (1994) 251

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, minor TeXnical revision to allow automatic TeXing

Scientific paper

10.1007/BF00805857

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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