Weight diagram

A diagram placing the weights of a representation in the real span of its weight lattice, recording each weight multiplicity. Coincident weights must retain their multiplicity: for an Adjoint representation the zero-weight multiplicity is the dimension of its Cartan subalgebra.

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- Tensor-product weight diagram Weight diagram

Tensor-product weight diagram ( $m_{V \otimes W} (μ) = \sum_{ν} m_{V} (μ - ν) m_{W} (ν)$ )

For a tensor product of Lie algebra representations with weight-space decompositions, the weights add and their weight multiplicities convolve. A diagram must sum contributions landing at the same weight, rather than treating coincident points as distinct positions.

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