The Cayley Grassmannian
  We study the projective variety CG parametrizing four dimensional subalgebras of the complex octonions, which we call the Cayley Grass-mannian. We prove that it is a spherical G2-variety with only three orbits that we describe explicitely. Its cohomology ring has a basis of Schubert type classes and we determine the intersection product completely. 
Laurent Manivel (I2M)
math.AG