The Ariki–Terasoma–Yamada tensor space and the blob algebra

We show that the Ariki–Terasoma–Yamada tensor module and its permutation submodules M(λ) are modules for the blob algebra when the Ariki–Koike algebra is a Hecke algebra of type B. We show that M(λ) and the standard modules Δ(λ) 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 Δ(λ) fails for M(λ), making M(λ) and Δ(λ) different modules in general. Finally, we prove that M(λ) is isomorphic to the dual Specht module for the Ariki–Koike algebra.