Let be a group and let be in the center of .

Why is for every irreducible representation of a scalair?

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- Dec 1st 2010, 01:56 AMbram kierkelsIrreducible representation
Let be a group and let be in the center of .

Why is for every irreducible representation of a scalair? - Dec 1st 2010, 01:00 PMDrexel28
- Dec 2nd 2010, 02:51 AMbram kierkels
rho is just an arbitrary representation, thus is a homomorphism on a (complex) vector space , where GL(V) is the general lineair group.

I think it is easier then it looks:

Since , and , it follows directly from this corollary of Schur's Lemma:

PlanetMath: Schur's lemma