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How can one write down the Haar measure of complex Grassmanians in terms of Plucker coordinates? Is there any way to define a Kahlarian measure like $d\mu\propto \det(g)dp_{ij}dp^{*}_{ij}$ where $g$ stands for the Grassmanian metric and $p_{ij}$ are the Plucker coordinates?

Thanks in advance AB

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