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 SLˉ(n,R), n=3,4 unitary irreducible representations is presented.
Infinite-component spinorial and tensorial SLˉ(4,R) fields,
"manifields", are introduced. Particle content of the ladder manifields, as
given by the SLˉ(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 Diffˉ(4,R) representations, that are constructed
explicitly.Comment: 19 pages, Te