THE CENTER OF A QUANTUM AFFINE ALGEBRA AT A ROOT OF UNITY

Using a recent extension of the Lusztig braid group automorphisms of a quantum affine algebra, I prove that at an odd l-th root of unity, the l-th power of every real root vector lies in the centre of the quantum affine algebra. The centre of a quantum affine algebra at a root of unity is infinite dimensional: nevertheless it is infinite dimensional over its centre.