27 pages, 9 captioned figures, 6 tables, authors from page 22 to page 24 ; see paper for full list of authors ; The inclusive production cross sections at forward rapidity of J/psi, psi(2S), Upsilon(1S) and Upsilon(2S) are measured in pp collisions at sqrt{s} = 7 TeV with the ALICE detector at the LHC. The analysis is based in a data sample corresponding to an integrated luminosity of 1.35 pb^-1. Quarkonia are reconstructed in the dimuon-decay channel and the signal yields are evaluated by fitting the mu+mu- invariant mass distributions. The differential production cross sections are measured as a function of the transverse momentum pt and rapidity y, over the ranges 0 < pt < 20 GeV/c for J/psi, 0 < pt < 12 GeV/c for all other resonances and for 2.5 < y < 4. The measured cross sections integrated over pt and y, and assuming unpolarized quarkonia, are: sigma_{J/psi} = 6.69 +- 0.04 +- 0.63 microbarn, sigma_{psiprime} = 1.13 +- 0.07 +- 0.14 microbarn, sigma_{Upsilon(1S)} = 54.2 +- 5.0 +- 6.7 nb and sigma_{Upsilon(2S)} = 18.4 +- 3.7 +- 2.2 nb, where the first uncertainty is statistical and the second one is systematic. The results are compared to measurements performed by other LHC experiments and to theoretical models.
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