  The usual ambient space approach to conformal fields is based on identifying
the d-dimensional conformal space as the Dirac projective hypercone in a flat
d+2-dimensional ambient space. In this work, we explicitly concentrate on
singletons of any integer spin and propose an approach that allows one to have
both locality and conformal symmetry manifest. This is achieved by using the
ambient space representation in the fiber rather than in spacetime. This
approach allows us to characterize a subalgebra of higher symmetries for any
bosonic singleton, which is a candidate higher-spin algebra for mixed symmetry
gauge fields on anti de Sitter spacetime. Furthermore, we argue that this
algebra actually exhausts all higher symmetries.
