Representations of $\mathfrak{s}\mathfrak{l}(2, \mathbb{C})$

Abstract

Unless otherwise indicated, in this chapter a representation of a Lie group or Lie algebra is a complex representation. We remind the reader that if $\mathfrak{g}$ is a complex Lie algebra [e.g. $\mathfrak{s}\mathfrak{l}(2, \mathbb{C})$], then a complex representation $\pi: \mathfrak{g} \rightarrow \mathop{\rm End}\nolimits (V )$ is assumed to be complex linear, while if $\mathfrak{g}$ is a real Lie algebra [e.g. $\mathfrak{s}\mathfrak{u}(2)$ or $\mathfrak{s}\mathfrak{l}(2, \mathbb{R})]$ then there is no such assumption.