A highest-weight vector is a nonzero weight vector annihilated by every positive-root raising operator. The module it generates is a highest-weight representation.
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- Weight vector
- Highest-weight representation
- Semisimple Lie algebra
- Lie algebra
- Lie theory
- Diagonal dominance
- Algebra
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- Adjoint representation of SU(3)
- Clebsch-Gordan splitting of a defining module and its cubic symmetric power
- Contraction splitting of a defining module tensor a dual symmetric square
- Crystal tensor-product rule
- Explicit weight basis of the exterior square of Sym4 for sl2
- Exterior and symmetric squares of the seven-dimensional G2 representation
- Highest-weight classification of finite-dimensional semisimple Lie algebra modules
- Level-two Virasoro descendant Gram matrix
- Maximum total angular momentum of equivalent fermions
- Normalized highest-weight lowering formula
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- sl2 tensor product of cubic and quadratic symmetric powers
- sl3 decomposition of the symmetric-square dual tensor product
- SU(3) quadratic Casimir eigenvalue
- Tensor contractions in the SU2 Clebsch-Gordan decomposition
- Traceless symmetric square of the defining even orthogonal representation
- Trace of a raising-lowering product in an irreducible sl2 module
- Unitary highest-weight termination
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