33 research outputs found
The Ariki-Terasoma-Yamada tensor space and the blob-algebra
We show that the Ariki-Terasoma-Yamada tensor module and its permutation
submodules are modules for the blob algebra when the Ariki-Koike
algebra is a Hecke algebra of type . We show that and the
standard modules 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 fails for , making and different modules in general. Finally, we prove that 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 and the blob algebra
(also known as the Temperley-Lieb algebra of type ) at roots of unity are -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 for the Specht modules of the
Iwahori-Hecke algebra of type . We focus on the base
change coefficients between the seminormal basis and Young's natural
basis 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