Cellular bases for algebras with a Jones basic construction
Abstract
We define a method which produces explicit cellular bases for algebras obtained via a Jones basic construction. For the class of algebras in question, our method gives formulas for generic Murphytype cellular bases indexed by paths on branching diagrams and compatible with restriction and induction on cell modules. The construction given here allows for a uniform combinatorial treatment of cellular bases and representations of the Brauer, BirmanMurakamiWenzl, TemperleyLieb, and partition algebras, among others.
 Publication:

arXiv eprints
 Pub Date:
 June 2011
 arXiv:
 arXiv:1106.5339
 Bibcode:
 2011arXiv1106.5339E
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory;
 20C08;
 16G99
 EPrint:
 43 pages. Includes figures created with tikz