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Published online by Cambridge University Press: 20 November 2018
We prove two spectral identities. The first one relates the relative trace formula for the spherical variety $\text{GSpin(4,}\,\text{3)/}{{G}_{2}}$ with a weighted trace formula for
$G{{L}_{2}}$. The second relates a spherical variety pertaining to
${{F}_{4}}$ to one of
$GSp\left( 6 \right)$. These identities are in accordance with a conjecture made by Jacquet, Lai, and Rallis, and are obtained without an appeal to a geometric comparison.