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We prove an orthogonality relation for the Fourier-Whittaker coefficients ofa thin family of $GL(3)$ Maass forms containing all self-dual forms. This isobtained by analysing the Kuznetsov trace formula on $GL(3)$ for a certainfamily of test functions. The method also yields Weyl's law for the same familyof Maass forms.

An orthogonality relation for a thin family of $GL(3)$ Maass forms