Weight diagrams of finite-dimensional irreducible representations of semisimple Lie algebras

Abstract

We review the representation theory of semisimple Lie algebras over the complex numbers, focusing on weight diagrams of representations of sl(3) and sp(4). There are two methods to obtain the weight diagram of a representation. The one is to consider the restriction to various sl(2)-subalgebras, and the other is to exploit the Verma modules. In the case of sl(3), we draw the weight diagrams of the standard representation of sl(3), its dual representation and the adjoint representation. In the case of sp(4), which is isomorphic to so(5), we draw the weight diagrams of the standard representation of sp(4), the standard representation of so(5) and the adjoint representation.