We consider the phase-space of Yang-Mills on a cylindrical space-time (S1×R) and the associated algebra of gauge-invariant functions, the
T-variables. We solve the Mandelstam identities both classically and
quantum-mechanically by considering the T-variables as functions of the
eigenvalues of the holonomy and their associated momenta. It is shown that
there are two inequivalent representations of the quantum T-algebra. Then we
compare this reduced phase space approach to Dirac quantization and find it to
give essentially equivalent results. We proceed to define a loop representation
in each of these two cases. One of these loop representations (for N=2) is
more or less equivalent to the usual loop representation.Comment: 15 pages, LaTeX, 1 postscript figure included, uses epsf.sty,
G\"oteborg ITP 93-3