Quotients of the affine Temperley-Lieb algebras with a view towards generalised Deligne interpolation categories

Abstract: The affine (and periodic) Temperley-Lieb algebras appeared in the study of conformal field theories as useful tools to study the continuum scaling limits of critical statistical models. The fusion of their modules is believed to be connected to the fusion of bulk fields in CFT. However, the connection is not obvious. In part to seek the ideal structure to investigate the scaling limit, we study certain quotients of the affine Temperley-Lieb algebras, which we name uncoiled algebras, and we study their Jones-Wenzl idempotents. In this talk, we will present the uncoiled algebras, the construction of their Jones-Wenzl idempotents and investigate the traces of these, relating it to the extremal weight projectors of Queffelec and Wedrich. Time permitting, we will investigate a generalisation of these structures related to Deligne interpolation categories.

This is based on joint work with Alexi Morin-Duchesne

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home