  The existence of a topological double-covering for the $GL(n,R)$ and
diffeomorphism groups is reviewed. These groups do not have finite-dimensional
faithful representations. An explicit construction and the classification of
all $\bar{SL}(n,R)$, $n=3,4$ unitary irreducible representations is presented.
Infinite-component spinorial and tensorial $\bar{SL}(4,R)$ fields,
"manifields", are introduced. Particle content of the ladder manifields, as
given by the $\bar{SL}(3,R)$ "little" group is determined. The manifields are
lifted to the corresponding world spinorial and tensorial manifields by making
use of generalized infinite-component frame fields. World manifields transform
w.r.t. corresponding $\bar{Diff}(4,R)$ representations, that are constructed
explicitly.
