On the Hiraga-Ichino-Ikeda conjecture on formal degrees for ${\mathrm{G}}_2$

Abstract

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 representation theory of ${\mathrm{PGSO}}_8$ with triality. A key feature of our approach is an application of the adjoint group of type $E_6$.

100 pages. A reference is added. Comments are welcome!