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

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.

8 pages, minor TeXnical revision to allow automatic TeXing

References in corpus (1)

• Composition of Kinetic Momenta: The U_q(sl(2)) case

Cited by in corpus (4)

• Representations of U_q(sl(N)) at Roots of Unity
• Quantum Matrix Models for Simple Current Orbifolds
• Quantum Supergroup $U_{r,s}(osp(1,2))$, Scasimir Operators, and Dickson polynomials
• Explicit Central Elements of $U_q(\mathfrak{gl}(N+1))$