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

Research paper by Steen Ryom-Hansen

Indexed on: 10 Mar '10Published on: 10 Mar '10Published in: Mathematics - Representation Theory

#### 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.