The multi-degree of coverings on Lie groups

Abstract

We associate to each covering map of simple Lie groups a sequence of integers, called the multi-degree of the covering; extend Schubert calculus to evaluate the invariant; and apply the results to solve two outstanding topological problems arising from the studies of the Wess-Zumino-Witten models and the topological Gauge theories. The main tool in our approach is the Chow rings of Lie groups, introduced by Grothendieck in 1958.