If on and on are irreducible representations and is a linear map such that for all and group , then or is invertible. Furthermore, if in a vector space over complex numbers, then is a scalar.
Schur's Representation Lemma
See also
Schur's LemmaExplore with Wolfram|Alpha
References
Knapp, A. W. "Group Representations and Harmonic Analysis, Part II." Not. Amer. Math. Soc. 43, 537-549, 1996.Referenced on Wolfram|Alpha
Schur's Representation LemmaCite this as:
Weisstein, Eric W. "Schur's Representation Lemma." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchursRepresentationLemma.html