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It has a geometric side which is a sum of distributions $I_{\\mathfrak{o}}(s, \\cdot)$ indexed by the invariants of the adjoint action of $\\mathrm{GL}_n(\\mathrm{F})$ on $\\mathfrak{gl}_{n+1}(\\mathrm{F})$ as well as a \"spectral side\" consisting of the Fourier transforms of the aforementioned distributions. 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