The (m, n) representations are (2 m + 1)(2 n + 1) -dimensional. This follows easiest from counting the dimensions in any concrete realization, such as the one given in representations of SL ( 2 , C ) and s l ( 2 , C ) . For a Lie general algebra g the Weyl dimension formula, dim ⁡ ⁡ π π ρ ρ = Π Π α α ∈ ∈ R + ⟨ ⟨ α α , ρ ρ + δ δ ⟩ ⟩ Π Π α α ∈ ∈ R + ⟨ ⟨ α α , δ δ ⟩ ⟩ , applies, where R is the set of positive roots, ρ is the highest weight, and δ is half the sum of the positive roots. The inner product ⟨ ⟨ ⋅ ⋅ , ⋅ ⋅ ⟩ ⟩ is that of the Lie algebra g , invariant under the action of the Weyl group on h ⊂ ⊂ g , the Cartan subalgebra. The roots (really elements of h ∗ ∗ ) are via this inner product identified with elements of h . For s l ( 2 , C ) , the formula reduces to dim π μ = 2 μ + 1 = 2 m + 1, where the present notation must be taken into account. The highest weight is 2 μ. By taking tensor products, the result follows.