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On the Hiraga-Ichino-Ikeda conjecture on formal degrees for $\mathrm{G_2}$
We prove that the twisted endoscopic character identities between triality $\mathrm{PGSO}_8$ and the endoscopic group $\mathrm{G}_2$ imply the Hiraga-Ichino-Ikeda conjecture on formal degrees for $\mathrm{G}_2$. In the course of proving the main result, we also establish some fundamental results on
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