Cellularity of a Larger Class of Diagram Algebras

2015/06/09 by N. Karimilla Bi, Bi, N. Karimilla
Mathematics · #16G30 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16G30

paper · pdf · doi:10.48550/arxiv.1506.02780

3 figures

arxiv created 2015/06/09 · arxiv updated 2015/06/10

Abstract

In this paper, we realize the algebra of ℤ₂-relations, signed partition algebras and partition algebras as tabular algebras and prove the cellularity of these algebras using the method of \citeGM1. Using the results of Graham and Lehrer in \citeGL, we give the modular representations of the algebra of ℤ₂-relations, signed partition algebras and partition algebras.

Related

• Constructing cell data for diagram algebras
• Cellularity and the Jones basic construction
• Branching rules for cell modules on a tower of the partition algebras
• Gram Matrices and Stirling numbers of a class of Diagram Algebras
• A cellular quotient of the Temperley--Lieb algebra of type D