A cellular analysis of the affine Temperley-Lieb algebras

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• Gus Isaac Lehrer (University of Sydney)
• Wednesday 28 June 2023, 09:00-10:00
• Seminar Room 1, Newton Institute.

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Abstract. We give two definitions of the affine Temperley-Lieb algebras, one (T Ldan(q)) as an affine Hecke algebra quotient, the other (Tan (q)) abstractly, as an endomorphism algebra in a category. The definitions are related by a one-parameter set {ϕα : T Ldan(q)−→Tan(q) | α ∈ C×} of surjections. The abstract versions have a diagrammatic presentation, and may be analysed using cellulartype theory: one constructs “cell modules”, (as functors) and classifies all natural transformations among them, leading to a classification of the simple modules (functors). These constructions are closely related to the Jones-Wenzl idempotents, and are intrinsic to Vaughan’s setting up of the theory of planar algebras. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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