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

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.Comment: Improved version

Graded cellular bases for Temperley-Lieb algebras of type A and B

We show that the Temperley-Lieb algebra of type $A$ and the blob algebra (also known as the Temperley-Lieb algebra of type $B$) at roots of unity are $\mathbb Z$-graded algebras.We moreover show that they are graded cellular algebras, thus making their cell modules, or standard modules, graded modules for the algebras.Comment: 36 pages. Final version, to appear in Journal of Algebraic Combinatoric

On the denominators of Young's seminormal basis

We study the seminormal basis ${f\_t}$ for the Specht modules of the Iwahori-Hecke algebra $\cal H\_{q,n}$ of type $A_{n-1}$. We focus on the base change coefficients between the seminormal basis ${f\_t}$ and Young's natural basis ${e\_t}$ with emphasis on the denominators of these coefficients. In certain important cases we obtain simple formulas for these coefficients involving radial lengths. Even for general tableaux we obtain new formulas. On the way we prove a new result about summands of the restricted Specht module at root of unity.Comment: 21 pages. The paper has been completely rewritten. The basic setting is now that of Iwahori-Hecke algebras of type $A