Under some conditions, if X and Y are both irreducible representations, then an intertwiner (other than the zero map) only exists if the two representations are equivalent (that is, are isomorphic as modules). That intertwiner is then unique up to a multiplicative factor (a non-zero scalar from K). These properties hold when the image of K [ G ] is a simple algebra, with centre K (by what is called Schur's lemma : see simple module). As a consequence, in important cases the construction of an intertwiner is enough to show the representations are effectively the same.