Cellular bases for algebras with a Jones basic construction
John Enyang, Frederick M. Goodman
TL;DR
This paper introduces a method to explicitly construct cellular bases for algebras derived from the Jones basic construction, unifying their combinatorial and representation-theoretic analysis.
Contribution
It provides a uniform combinatorial framework for cellular bases of various algebras using the Jones basic construction, including Brauer and Temperley-Lieb algebras.
Findings
Explicit formulas for Murphy-type cellular bases
Compatibility with restriction and induction processes
Unified approach for multiple algebra classes
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.
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