On some geometrical consequences of physical symmetries

Abstract

It is shown that there exists only one submanifold O (4, m) 2 of the representation space C 4m of the group GL(4, C)× GL( m, C) which admits a unique projection onto Minkowski space, consistent with the group. We describe the decomposition of this manifold O 4, m) 2 when the group is restricted to the physical symmetry group SU (2,2)× × SU( m) or P× SU( m). We consider also representations of SU(2,2)× SU( m) in the resulting submanifolds and in the Hilbert space of functions over these manifolds.