The complex linear representations of formula_5 and formula_2 are more straightforward to obtain than the formula_130 representations. They can be (and usually are) written down from scratch. The holomorphic group representations (meaning the corresponding Lie algebra representation is complex linear) are related to the complex linear Lie algebra representations by exponentiation. The real linear representations of formula_5 are exactly the -representations. They can be exponentiated too. The -representations are complex linear and are (isomorphic to) the highest weight-representations. These are usually indexed with only one integer (but half-integers are used here).