CENTERS AND COXETER ELEMENTS

Abstract. Suppose that G is a connected compact Lie group. We show that simple numerical information about the Weyl group of G can be used to obtain bounds, often sharp, on the size of the center of G. These bounds are obtained with the help of certain Coxeter elements in the Weyl group. Variants of the method use generalized Coxeter elements and apply to p-compact groups; in this case a splitting theorem emerges. The Lie group results are mostly known, but our arguments have a conceptual appeal. 1