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