  We show that the Ariki-Terasoma-Yamada tensor module and its permutation
submodules $ M(\lambda) $ are modules for the blob algebra when the Ariki-Koike
algebra is a Hecke algebra of type $B$. We show that $ M(\lambda)$ and the
standard modules $ \Delta(\lambda) $ have the same dimensions, the same
localization and similar restriction properties and are equal in the
Grothendieck group. Still we find that the universal property for $
\Delta(\lambda) $ fails for $ M(\lambda) $, making $ M(\lambda) $ and $
\Delta(\lambda) $ different modules in general. Finally, we prove that $
M(\lambda) $ is isomorphic to the dual Specht module for the Ariki-Koike
algebra.
