Highest-weight character subtraction
= Highest-weight character subtraction
For a finite-dimensional representation of a complex <semisimple Lie algebra>, select a maximal remaining <dominant weight>, subtract that multiplicity of the corresponding irreducible <formal character>, and repeat. The <Weyl complete reducibility theorem> guarantees nonnegative residual multiplicities and termination. Checking the full character or the exhausted total dimension confirms that no summands remain.