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

Abstract

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.

Improved version.

Cited by in corpus (1)

• On the Representation Theory of an Algebra of Braids and Ties