Schur's lemma for irreducible representations over the complex numbers states that if a matrix commutes with all matrices of the representation then it is a (complex) multiple of the identity matrix, that is, the set of commuting matrices is isomorphic to the complex numbers C . The equivalent of Schur's lemma for irreducible corepresentations is that the set of commuting matrices is isomorphic to R , C or the quaternions Q . Using the intertwining number [1] over the real numbers, this may be expressed as an intertwining number of 1, 2 or 4.