Prove Schur 's lemma a matrix that commutes with all generators of an irrep is a multiple of the unit matrix Hint Assume that ( left T a , M ight 0 ) for all (a ), where (T a ) is a group generator and (M ) is some matrix Show that there is a contradiction unless every member of the irrep has the same eigenvalue with respect to (M )

Question: Prove Schur's lemma: a matrix that commutes with all generators of an irrep is a multiple of the unit matrix. Hint: Assume that (left[T_{a}, M

Prove Schur's lemma: a matrix that commutes with all generators of an irrep is a multiple of the unit matrix. Hint: Assume that $\left[T_{a}, M\right]=0$ for all $a$, where $T_{a}$ is a group generator and $M$ is some matrix. Show that there is a contradiction unless every member of the irrep has the same eigenvalue with respect to $M$.

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