Cellular bases for algebras with a Jones basic construction

Details Cellular bases for algebras with a Jones basic construction Cellular bases for algebras with a Jones basic construction

2011-06-27

arxiv.org/abs/1106.5339v2

Mathematics

Quantum Algebra

27 pages, 7 figures; corrected typos from version 1

Scientific paper

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 formulae 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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