Schur's Lemmas are as follows:
1. unitary representatio D irreducible <=> only matrics commuting with all D(g) =cI <=> (D(g)A=AD(g) forall g in G => A=cI

2. D1(g),D2(g) irreps of dim n1, dim n2 /\ there exists n1xn2 A s.t. D1(g)A=AD2(g) forall g in G => A=0 or n1=n2 and D1 and D2 are equivalent.