New Integrable Lattice Models From Fuss-Catalan Algebras

P. Di Francesco

New Integrable Lattice Models From Fuss-Catalan Algebras

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arxiv hep-th/9807074 v1 pith:HBCUVO7X submitted 1998-07-10 hep-th cond-mat.stat-mechmath.QA

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keywords algebrasfuss-catalanintegrablelatticemodelsalgebrabischcolored

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We construct new trigonometric solutions of the Yang-Baxter equation, using the Fuss-Catalan algebras, a set of multi-colored versions of the Temperley-Lieb algebra, recently introduced by Bisch and Jones. These lead to new two-dimensional integrable lattice models, describing dense gases of colored loops.

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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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