[tex]D(g)[/tex] is a representaiton of a group denoted by [tex]g[/tex]. The representaion is recucible if it has an invariant subspace, which means that the action of any [tex]D(g)[/tex] on any vector in the subspace is still in the subspace. In terms of a projection operator [tex]P[/tex] onto the subspace this condition can be written as [tex]PD(g)P=D(g)P~~~~~\forall~g\inG[/tex]. And furthermore the conditon can be converted into [tex]D(g)P=P~~~~~\forall~g[/tex]. I don't know why the complex condition can be converted into the short and simple one. Can you tell me, thanks a lot.