Products of conjugacy classes in simple algebraic groups in terms of diagrams

Abstract

For a simple algebraic group G over an algebraically closed field we study products of normal subsets. For this we mark the nodes of the Dynkin diagram of G. We use two types of labels, a binary marking and a labeling with non-negative integers. The first is used to recognize large conjugacy classes which appear in a product of two conjugacy classes while the second is used to keep track of multiplicities of regular diagrams. In particular, we formulate sufficient conditions in terms of marked diagrams, for a product of normal subsets in G to contain regular semisimple elements.