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

Steen Ryom-Hansen
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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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BibTeXRIS

Steen Ryom-Hansen. 2010-03-11. The Ariki-Terasoma-Yamada tensor space and the blob-algebra. https://arxiv.org/abs/math/0505278

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