(b) Let C[G] be the regular representation of the finite group G, let Vį be an irreducible representation of G with char

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B Let C G Be The Regular Representation Of The Finite Group G Let Vi Be An Irreducible Representation Of G With Char 1 (125.24 KiB) Viewed 14 times

(b) Let C[G] be the regular representation of the finite group G, let Vį be an irreducible representation of G with character Xv₁, and C[G] → C[G] defined as above: x₁(g)p(g). ox₁ = bx gEG Use Schur's Lemma to prove that the image of o, is the sum of all irreducible representations isomorphic with V; in C[G].