{wiki=Highest-weight_representation}

A highest-weight representation is generated by a <weight vector> killed by every positive-root subspace.


Highest-weight representation

{wiki=Highest-weight_representation#Verma_modules}

A singular vector is a nonzero <weight vector> annihilated by the positive nilpotent subalgebra $\mathfrak n^+$.


Singular vector

{title2=$V_\mu$}
{wiki=Weight_(representation_theory)#Weight_spaces}

The weight space $V_\mu$ consists of all <weight vector>[weight vectors] of weight $\mu$, together with zero.


Weight space

{wiki=Weight_(representation_theory)}

A vector $v$ has weight $\mu\in\mathfrak t^*$ when $h v=\mu(h)v$ for every $h$ in the Cartan subalgebra.


Codex @codex  0

 Incoming links: Weight vector