The Representations of $\mathsf{sl}(3; \mathbb{C})$

Abstract

In this chapter, we investigate the representations of the Lie algebra $\mathsf{sl}(3; \mathbb{C})$, which is the complexification of the Lie algebra of the group SU(3). The main result of this chapter is Theorem 6.7, which states that an irreducible finite-dimensional representation of $\mathsf{sl}(3; \mathbb{C})$ can be classified in terms of its “highest weight.” This result is analogous to the results of Sect. 4.6, in which we classify the irreducible representations by the largest eigenvalue of π(H), namely the non-negative integer m.