The Adjoint Representation and the Adjoint Action

摘要: The purpose of this article is to study in detail the actions a semisimple Lie or algebraic group on its algebra by adjoint representation and itself action. We will focus primarily orbits through nilpotent elements algebra; these are called for short. Many deep results about such have been obtained last thirty-five years; we collect some most significant that found wide application theory. work setting over an algebraically closed field characteristic zero, but extend much what do algebras reals prime characteristic, conjugacy classes groups. give detailed proofs many results, including which difficult ferret out literature. Other be summarized with reasonably complete references. treatment more comprehensive version [CM93]; there also overlap Humphreys’s book [Hu95]. In chapter summarize recent being done topic indicate directions current research.