Gauge fields in (A)dSd and connections of its symmetry algebra

The generalized connections of the de Sitter algebra so(d, 1) and anti-de Sitter algebra so(d-1, 2), which are differential forms of arbitrary degree with values in any irreducible (spin)-tensor representation of the (anti)-de Sitter algebra, are studied. It is shown that an arbitrary-spin gauge field in (anti)-de Sitter space, massless or partially-massless, can be described by a single connection. A 'one-to-one' correspondence between the connections of the (anti)-de Sitter algebra and the gauge fields is established. The gauge symmetry is manifest and auxiliary fields are automatically included in the formalism.