  The 21cm-galaxy cross-power spectrum is expected to be one of the promising
probes of the Epoch of Reionization (EoR), as it could offer information about
the progress of reionization and the typical scale of ionized regions at
different redshifts. With upcoming observations of 21cm emission from the EoR
with the Low Frequency Array (LOFAR), and of high redshift Lyalpha emitters
(LAEs) with Subaru's Hyper Suprime Cam (HSC), we investigate the observability
of such cross-power spectrum with these two instruments, which are both
planning to observe the ELAIS-N1 field at z=6.6. In this paper we use N-body +
radiative transfer (both for continuum and Lyalpha photons) simulations at
redshift 6.68, 7.06 and 7.3 to compute the 3D theoretical 21cm-galaxy
cross-power spectrum, as well as to predict the 2D 21cm-galaxy cross-power
spectrum expected to be observed by LOFAR and HSC. Once noise and projection
effects are accounted for, our predictions of the 21cm-galaxy cross-power
spectrum show clear anti-correlation on scales larger than ~ 60 h$^{-1}$ Mpc
(corresponding to k ~ 0.1 h Mpc$^{-1}$), with levels of significance p=0.04 at
z=6.6 and p=0.048 at z=7.3. On smaller scales, instead, the signal is
completely contaminated.
