If "G" is group with Lie algebra formula_3, every finite-dimensional representation of "G" induces a representation of formula_3. A weight of the representation of "G" is then simply a weight of the associated representation of formula_3. There is a subtle distinction between weights of group representations and Lie algebra representations, which is that there is a different notion of integrality condition in the two cases; see below. (The integrality condition is more restrictive in the group case, reflecting that not every representation of the Lie algebra comes from a representation of the group.)