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The Blob Algebra and the Periodic Temperley-Lieb Algebra

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arxiv hep-th/9302094 v1 pith:IJU6UTEG submitted 1993-02-19 hep-th

Paul Martin , Hubert Saleur This is my paper · ORCID
classification hep-th
keywords algebrablobstructuretemperley-liebdetermineexceptionalgenericperiodic
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We determine the structure of two variations on the Temperley-Lieb algebra, both used for dealing with special kinds of boundary conditions in statistical mechanics models. The first is a new algebra, the `blob' algebra (the reason for the name will become obvious shortly!). We determine both the generic and all the exceptional structures for this two parameter algebra. The second is the periodic Temperley-Lieb algebra. The generic structure and part of the exceptional structure of this algebra have already been studied. Here we complete the analysis, using results from the study of the blob algebra.

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Cited by 3 Pith papers

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  1. Logarithmic correlation functions for critical dense polymers on the cylinder

    cond-mat.stat-mech 2019-07 unverdicted novelty 7.0 of 10

    Explicit finite-n lattice correlators for dense polymers on a cylinder are computed via Temperley-Lieb algebra and shown to match ratios of c=-2 CFT correlators involving boundary fields of dimensions -1/8 and 0, with...

  2. Universal TT- and TQ-relations via centrally extended q-Onsager algebra

    math.QA 2025-11 unverdicted novelty 6.0 of 10

    Universal TT- and TQ-relations are derived for the centrally extended q-Onsager algebra, giving explicit polynomials for local conserved quantities in spin-j chains and new symmetries for special boundaries.

  3. Fuss--Catalan algebras on generalized Dyck paths via non-crossing partitions

    math.CO 2025-07 conditional novelty 6.0 of 10

    Fuss-Catalan algebras and their one- and two-boundary versions are realized on increasing chains of non-crossing partitions, with a new r=2 reflection equation solution.

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