Casimir eigenvalue
= Casimir eigenvalue
{c}
{title2=$c_\lambda=(\lambda,\lambda+2\rho)$}
The <Casimir operator> formed from the <Killing form> acts on an <Irreducible Lie algebra representation> with <highest weight> $\lambda$ by the scalar $(\lambda,\lambda+2\rho)$, where $\rho$ is the <half-sum of positive roots>. It is zero on the <trivial Lie algebra representation> and nonzero on every nontrivial finite-dimensional irreducible complex representation of a <semisimple Lie algebra>.