Schur's Representation Lemma

If $\pi$ on $V$ and $\pi'$ on $V'$ are irreducible representations and $E:V\mapsto V'$ is a linear map such that $\pi'(g)E=E\pi(g)$ for all $g\in$ and group $G$, then $E=0$ or $E$ is invertible. Furthermore, if $V=V'$, then $E$ is a Scalar.

References

Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.