= Generalized weight space of a Lie algebra representation
{title2=$V^\lambda=\{v:(\rho(h)-\lambda(h)I)^{\dim V}v=0\ \forall h\}$}
= Generalized weight space
{synonym}
For a finite-dimensional complex <Lie algebra representation> $\rho$ of a <nilpotent Lie algebra> $H$, a generalized weight space is the simultaneous generalized <eigenspace> displayed above, where $\lambda:H\to\mathbb C$ is a <linear functional>. Every occurring $\lambda$ vanishes on the <derived algebra> of $H$. Ordinary <weight vectors> satisfy the same equations without the powers.
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