We adopt the concept of the composite parameterization of the unitary group |$\mathcal {U}(d)$| to the special unitary group |$\mathcal {SU}(d)$|. Furthermore, we also consider the Haar measure in terms of the introduced parameters. We show that the well-defined structure of the parameterization leads to a concise formula for the normalized Haar measure on |$\mathcal {U}(d)$| and |$\mathcal {SU}(d)$|. With regard to possible applications of our results, we consider the computation of high-order integrals over unitary groups.
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The order of the product is
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2012
American Institute of Physics
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