Generalized Temperley-Lieb algebras and decorated tangles

R.M. Green

Generalized Temperley-Lieb algebras and decorated tangles

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arxiv q-alg/9712018 v1 pith:MA2BD7CH submitted 1997-12-04 q-alg math.QA

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keywords temperley-liebalgebraalgebrasanaloguesassociatedcalculuscoxeterdecorated

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abstract

We give presentations, by means of diagrammatic generators and relations, of the analogues of the Temperley-Lieb algebras associated as Hecke algebra quotients to Coxeter graphs of type B and $D$. This generalizes Kauffman's diagram calculus for the Temperley-Lieb algebra.

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Jones--Wenzl projections of type $D$ and Dyck tilings
math.CO 2024-12 conditional novelty 6.0 of 10

Coefficients of the type D Jones-Wenzl projection are expressed as generating functions over Dyck tilings decorated with bi-colored vertical Hermite histories, for both even and odd dot cases.

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