  We use Lie-algebraic arguments to classify Lorentz-invariant theories of
massless interacting scalars that feature coordinate-dependent redundant
symmetries of the Galileon type. We show that such theories are determined, up
to a set of low-energy effective couplings, by specifying an affine
representation of the Lie algebra of physical, non-redundant internal
symmetries and an invariant metric on its target space. This creates an
infinite catalog of theories relevant for both cosmology and high-energy
physics thanks to their special properties such as enhanced scaling of
scattering amplitudes in the soft limit.
