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Schur's Representation Lemma


If pi on V and pi^' on V^' are irreducible representations and E:V|->V^' is a linear map such that pi^'(g)E=Epi(g) for all g in and group G, then E=0 or E is invertible. Furthermore, if V=V^' in a vector space over complex numbers, then E is a scalar.


See also

Schur's Lemma

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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 Lemma

Cite this as:

Weisstein, Eric W. "Schur's Representation Lemma." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchursRepresentationLemma.html

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