THE SPHERE S⁶ VIEWED AS A G₂/SU(3) COSET SPACE

By deriving an explicit and strikingly tractable parametrisation of the coset space G₂/SU(3), this paper develops a non-linear realisation of G₂ in which its SU(3) subgroup is realised linearly. Since SU(3) is not a symmetric subalgebra of G₂ the situation differs from that found for examples like chiral G⊗G or symmetric space G/H examples. Despite this the treatment exhibits great simplicity, some aspects of which stem from the parametrisation found. The well-known relationship of the coset space G₂/SU(3) to the SO(7)/SO(6) description of the sphere S⁶ emerges and provides explicitly the relative scale factor of the quadratic Casimir operators of G₂ and SO(7) inherent in the formalism.