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A group symmetry analysis of the low lying levels of the spin-1/2 kagom\'eHeisenberg antiferromagnet is performed for small samples up to N=27. Thisapproach allows to follow the effect of quantum fluctuations when the samplesize increases. The results contradict the scenario of ``order by disorder''which has been advanced on the basis of large S calculations. A large enoughsecond neighbor ferromagnetic exchange coupling is needed to stabilize the$\sqrt 3 \times \sqrt 3$ pattern: the finite size analysis indicates a quantumcritical transition at a non zero coupling.Comment: 21 pages, Revte

Order versus disorder in the quantum Heisenberg antiferromagnet on thekagomélattice using exact spectra analysis