The reduction of higher-dimensional theories over a coset space S/R is known to yield a residual gauge symmetry related to the number of R-singlets in the decomposition of S with respect to R. It is verified that this invariance is identical to that found by requiring that there is a subgroup of the isometry group with an action on the connection form that yields a transformation rule defined only on the base space. The Lagrangian formulation of the projection of the frame of global vector fields from S7 to the Lie group submanifold S3× S3 is considered. The structure of an octonionic Chern-Simons gauge theory is described.
"Reduction over Coset Spaces and Residual Gauge Symmetry." J. Gen. Lie Theory Appl. 10 (1) 1 - 8, 2016. https://doi.org/10.4172/1736-4337.1000249