  We investigate the role of two- and three-body $\Lambda$-nucleon forces by
computing the ground state of a few $\Lambda$-hypernuclei with the Auxiliary
Field Diffusion Monte Carlo algorithm. Calculations have been performed for
masses up to A=41, including some open-shell hypernuclei. The results show that
the use of a bare hyperon-nucleon force fitted on the available scattering data
yields a consistent overestimate of the $\Lambda$-separation energy
$B_\Lambda$. The inclusion of a hyperon-nucleon-nucleon interaction
systematically reduces $B_\Lambda$, leading to a qualitatively good agreement
with experimental data over the range of masses investigated.
