Classes of unipotent elements in simple algebraic groups. I

Abstract

Let G be a simple adjoint algebraic group over an algebraically closed field K . We are concerned to describe the conjugacy classes of unipotent elements of G. G operates on its Lie algebra g by means of the adjoint action and we may consider classes of nilpotent elements of g under this action. It has been shown by Springer (11) that there is a bijection between the unipotent elements of G and the nilpotent elements of g which preserves the G -action, provided that the characteristic of K is either 0 or a ‘good prime’ for G . Thus we may concentrate on the problem of classifying the nilpotent elements of g under the adjoint G -action.