On Cellular Algebras with Jucys Murphy Elements

2009/07/20 by Frederick M. Goodman, Goodman, Frederick M., John Graber +1
Mathematics · #16G99 #20C08 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:16G99 #msc:20C08 #msc:81R50

paper · pdf · doi:10.48550/arxiv.0907.3459

Improved and reorganized exposition. Some new results

arxiv created 2010/11/15 · arxiv updated 2010/11/16

Abstract

We study analogues of Jucys-Murphy elements in cellular algebras arising from repeated Jones basic constructions. Examples include Brauer and BMW algebras and their cyclotomic analogues.

Related

• Cellularity and the Jones basic construction
• Cellular bases for algebras with a Jones basic construction
• Graded cellular basis and Jucys-Murphy elements for generalized blob\n algebras
• The representations of cyclotomic BMW algebras
• Cellularity of cyclotomic Yokonuma-Hecke algebras