  Using the results from a previously developed Lyman Alpha/continuum
production/transmission and dust enrichment model for Lyman Alpha Emitters
(LAEs), based on cosmological SPH simulations, we assess the detectability of
their dust-reprocessed sub-millimeter (submm) radiation. As supernovae (rather
than evolved stars) control dust formation and destruction processes, LAEs are
relatively dust-poor with respect to local galaxies: they have low dust-to-gas
ratios (0.05 times the dust-to-gas ratio of the Milky Way) in spite of their
relatively high metallicity, which is approximately 10-50% of the solar value.
Using the derived escape fraction of ultraviolet (UV) continuum photons we
compute the UV luminosity absorbed by dust and re-emitted in the far infrared.
The LAE submm fluxes correlate with their Lyman Alpha luminosity: about (3%,
1%) at z=(5.7, 6.6) of the LAEs in our simulated sample (those with with Log
L_\alpha > 43.1) would have fluxes at 850 micrometer (the optimal band for
detection) in excess of 0.12 mJy and will be therefore detectable at 5 sigma
with ALMA with an integration time of only 1 hour. Such detections would open a
new window on the physical conditions prevailing in these most distant
galaxies.
