Polynomial Relations in the Centre of U_q(sl(N))
High Energy Physics - Theory
2009-10-22 v1 Quantum Algebra
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.
Cite
@article{arxiv.hep-th/9310030,
title = {Polynomial Relations in the Centre of U_q(sl(N))},
author = {Daniel Arnaudon and Michel Bauer},
journal= {arXiv preprint arXiv:hep-th/9310030},
year = {2009}
}
Comments
8 pages, minor TeXnical revision to allow automatic TeXing