Exotic holonomies $\E_7^{(a)}$

Q. -S. Chi, S. A. Merkulov, L. J. Schwachhöfer

It is proved that the Lie groups $\E_7^{(5)}$ and $\E^{(7)}_7$ represented in ${\mathbb{R}}^{56}$ and the Lie group $\E_7^{\C}$ represented in ${\mathbb{R}}^{112}$ occur as holonomies of torsion-free…