Prove Schur's lemma: a matrix that commutes with all generators of an irrep is a multiple of
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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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Related Book For
Symmetry Broken Symmetry And Topology In Modern Physics A First Course
ISBN: 9781316518618
1st Edition
Authors: Mike Guidry, Yang Sun
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