Cellular bases for algebras with a Jones basic construction
Quantum Algebra
2015-04-06 v7 Representation Theory
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 Murphy--type 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, Birman-Murakami-Wenzl, Temperley-Lieb, and partition algebras, among others.
Keywords
Cite
@article{arxiv.1106.5339,
title = {Cellular bases for algebras with a Jones basic construction},
author = {John Enyang and Frederick M. Goodman},
journal= {arXiv preprint arXiv:1106.5339},
year = {2015}
}
Comments
43 pages. Includes figures created with tikz