  IIB supergravity is reformulated with a manifest local USp(8) invariance that
makes the embedding of five-dimensional maximal supergravities transparent. In
this formulation the ten-dimensional theory exhibits all the 27 one-form fields
and 22 of the 27 two-form fields that are required by the vector-tensor
hierarchy of the five-dimensional theory. The missing 5 two-form fields must
transform in the same representation as a descendant of the ten-dimensional
`dual graviton'. The invariant E6(6) symmetric tensor that appears in the
vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from
the supersymmetry transformations of the vector fields, as well as consistent
expressions for the USp(8) covariant fermion fields. Implications are discussed
for the consistency of the truncation of IIB supergravity compactified on the
five-sphere to maximal gauged supergravity in five space-time dimensions with
an SO(6) gauge group.
