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Irreducible representation proofs

1. Assume that the field is algebraically closed and has zero characteristic, G is finite and representations are finite-dimensional.

Show that this statement is true under the above assumptions:

"Let p be an irreducible representation of G, and q be an irreducible representation of H. Is it always true that the exterior tensor product of p and q is an irreducible representation of G X H?"

2. Let p: G -> GL(V) be a representation. Show that each irreducible subrepresentation of V has multiplicity 1 iff EndG(V) is a commutative ring.

Solution Summary

There are two proofs here regarding irreducible representations.