Cellularity and the Jones basic construction

Details Cellularity and the Jones basic construction Cellularity and the Jones basic construction

2009-06-08

arxiv.org/abs/0906.1496v2

Mathematics

Representation Theory

Revised introduction and improved treatment of cyclotomic BMW algebras. To appear in Advances in Applied Mathematics.

Scientific paper

We establish a framework for cellularity of algebras related to the Jones basic construction. Our framework allows a uniform proof of cellularity of Brauer algebras, ordinary and cyclotomic BMW algebras, walled Brauer algebras, partition algebras, and others. Our cellular bases are labeled by paths on certain branching diagrams rather than by tangles. Moreover, for the class of algebras that we study, we show that the cellular structures are compatible with restriction and induction of modules. Applied to cyclotomic BMW algebras, our method allows a new a shorter proof of the finite spanning result and isomorphism with cyclotomic Kauffman tangle algebras.

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