Abstract
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.
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