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

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

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

Authors

Chi, Q. -S.

Merkulov, S. A.

Schwachhöfer, L. J.

Description

It is proved that the Lie groups $\E_7^{(5)}$ and $\E^{(7)}_7$ represented in $\R^{56}$ and the Lie group $\E_7^{\C}$ represented in $\R^{112}$ occur as holonomies of torsion-free affine connections. It is also shown that the moduli spaces of torsion-free affine connnections with these holonomies are finite dimensional, and that every such connection has a local symmetry group of positive dimension.
LaTeX, 10 pages