Weight-space decomposition
= Weight-space decomposition
{title2=$V=\bigoplus_\mu V_\mu$}
A weight-space decomposition expresses a <Lie algebra representation> as a <direct sum> of simultaneous <eigenspaces> for a <Cartan subalgebra>. Each summand is the <weight space> for its <weight>. In complex finite-dimensional representations of a <semisimple Lie algebra>, the simple <coroots> act as commuting diagonalizable operators, giving this decomposition.