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

Abstract

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.

36 pages. Final version, to appear in Journal of Algebraic Combinatorics

References in corpus (4)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Graded Specht modules
• Graded decomposition numbers for the blob algebra

Cited by in corpus (1)

• Graded decomposition numbers for the blob algebra