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arXiv · 1106.5339

Cellular bases for algebras with a Jones basic construction

John Enyang·Frederick M. Goodman
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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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John Enyang, Frederick M. Goodman. 2015-04-03. Cellular bases for algebras with a Jones basic construction. https://arxiv.org/abs/1106.5339

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