  We study the exact low energy spectra of the spin 1/2 Heisenberg
antiferromagnet on small samples of the kagom\'e lattice of up to N=36 sites.
In agreement with the conclusions of previous authors, we find that these low
energy spectra contradict the hypothesis of N\'eel type long range order.
Certainly, the ground state of this system is a spin liquid, but its properties
are rather unusual. The magnetic ($\Delta S=1$) excitations are separated from
the ground state by a gap. However, this gap is filled with nonmagnetic
($\Delta S=0$) excitations. In the thermodynamic limit the spectrum of these
nonmagnetic excitations will presumably develop into a gapless continuum
adjacent to the ground state. Surprisingly, the eigenstates of samples with an
odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries
which could support long range chiral order. We do not know if these states
will be true thermodynamic states or only metastable ones. In any case, the low
energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagom\'e
lattice clearly distinguish this system from either a short range RVB spin
liquid or a standard chiral spin liquid. Presumably they are facets of a
generically new state of frustrated two-dimensional quantum antiferromagnets.
