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I would like to compute the area of some subspaces of $SU(n)^d$ defined by group equation (basically $U_{i_1}^{e_1}\dots U_{i_k}^{e_k}=1$) . I know that there is the function RegionMeasure that computes measures, but how can I define $SU(n)$ as a region? Also, is there some packages or something usefull for such explicit integrale computations on Lie groups/ riemannian manifolds?

I am very new at mathematica, so please go easy on me.

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