# Highest Weight Representations

The representations of Lie algebras and connected reductive Lie groups are classified by *highest weights*. In addition to being able to construct these representations [[de Graaf, 2001](../../references.md#cite-wdg-lie-hwrep)], we can compute the combinatorics of their weights. This includes all the functionality of the LiE system [[van Leeuwen *et al.*, 1992](../../references.md#cite-leeuwen-cohen-lisser)]. This is described in Chapter [Representations of Lie Groups and Algebras](../RepresentationsOfLieGroupsAndAlgebras/index-representations-of-lie-groups-and-algebras.md#chapliereps).