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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.


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

© 1996-9 Eric W. Weisstein