Schur's representation lemma states that if 
on 
and 
on 
are irreducible
representations of a group 
and 
is a linear
map such that 
for all 
, then 
or 
is invertible. Furthermore,
if 
and 
is a finite-dimensional vector space over the complex numbers, then 
is a scalar multiple of the identity map.
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 Resource. https://mathworld.wolfram.com/SchursRepresentationLemma.html