The Sphere S⁶viewed as a G₂/Su(3) Coset Space

By deriving an explicit and strikingly tractable parametrisation of the coset space G 2 / SU (3), this paper develops a non-linear realisation of G 2 in which its SU(3) subgroup is realised linearly. Since SU(3) is not a symmetric subalgebra of G 2 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 G 2 / SU (3) to the SO (7)/ SO (6) description of the sphere S 6 emerges and provides explicitly the relative scale factor of the quadratic Casimir operators of G 2 and SO(7) inherent in the formalism.