More generally, in the representation theory of semisimple Lie algebras (or the closely related representation theory of compact Lie groups), the weights of the dual representation are the "negatives" of the weights of the original representation. (See the figure.) Now, for a given Lie algebra, if it should happen that operator formula_17 is an element of the Weyl group, then the weights of every representation are automatically invariant under the map formula_18. For such Lie algebras, "every" irreducible representation will be isomorphic to its dual. (This is the situation for SU(2), where the Weyl group is formula_19.) Lie algebras with this property include the odd orthogonal Lie algebras formula_20 (type formula_21) and the symplectic Lie algebras formula_22 (type formula_23).