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I Question about Haar measures on lie groups

  1. Jul 12, 2017 #1
    I'm not sure if this question belongs to here, but here it goes

    Suppose you have to integrate over a lie group in the fundamental representation. If you pass to the adjoint representation of that group, does the Haar measure have to change? I think that it should not change because it is invariant under left and right translations, is it correct?
  2. jcsd
  3. Jul 12, 2017 #2


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    Integrate what?
  4. Jul 12, 2017 #3
    Some function f: G -> ℝ, where G is the Lie group. For example, the Itzykson-Zuber integral

    ∫dUexp(-tr(XUYU)), where X, Y are n x n hermitean matrices and U ∈ U(n)
  5. Jul 16, 2017 #4


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  6. Jul 16, 2017 #5
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