The General Setup: Analyzing the Structure and Representations of an Arbitrary Semisimple Lie Algebra

Abstract

This is the last of the four central lectures; in the body of it, §14.1, we extract from the examples of §11-13 the basic algorithm for analyzing a general semisimple Lie algebra and its representations. It is this algorithm that we will spend the remainder of Part III carrying out for the classical algebras, and the reader who finds the general setup confusing may wish to read this lecture in parallel with, for example, Lectures 15 and 16. In particular, §14.2 is less clearly motivated by what we have worked out so far; the reader may wish to skim it for now and defer a more thorough reading until after going through some more of the examples of Lectures 15-20.