Cayley 4-frames and a quaternion-Kähler reduction related to Spin(7)

Abstract

We describe an action of $U(1)\times Sp(1)$ on $H{P}^7$ that allows to obtain a $Z_2$-quotient of CAYLEY (the Grassmannian of oriented 4-planes in $R^8$ closed under the three-fold cross product) by quaternionic Kähler reduction.

To appear in: Proceedings of the International Congress of Differential Geometry in the memory of A. Gray, held in Bilbao, Sept. 2000; Contemp. Math., AMS 2001