The Principle of Triality and A Distinguished Unitary Representation of SO(4,4)

Abstract

The group SO(4,2) is a familiar symmetry group in physics since among other things it is the conformal group of compactified Minkowski space S ³ x S ¹. The double covering SU(2,2) of its identity component SO(4,2) _e appears as a subgroup of the symmetry group Sp(8, R). In fact, if one considers the real and imaginary part of the Hermitian form in C ⁴ with signature ++--H one sees immediately that

$$U\left( {2,2} \right) = Sp\left( {8,R} \right) \cap SO\left( {4,4} \right) $$

(1)

This paper was supported in part by the NSF Grant No. DMS8403203