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VOL. 80 | 2019 Dual bases in Temperley-Lieb algebras
Michael Brannan, Benoît Collins

Editor(s) Masaki Izumi, Yasuyuki Kawahigashi, Motoko Kotani, Hiroki Matui, Narutaka Ozawa

## Abstract

This note is an announcement of the paper [BC16]. We derive a Laurent series expansion in $d$ for the structure coefficients appearing in the dual basis corresponding to the Kauffman diagram basis of the Temperley-Lieb algebra $\mathrm{TL}_k(d)$, converging for all complex loop parameters $d$ with $|d| \gt 2\cos\big(\frac{\pi}{k+1}\big)$. The coefficients appearing in each Laurent expansion are shown to have a natural combinatorial interpretation and their sign is explicitly understood. As an application, we solve a series of questions raised by Jones and improve substantially our understanding of the Jones Wenzl projection.

## Information

Published: 1 January 2019
First available in Project Euclid: 21 August 2019

zbMATH: 07116421
MathSciNet: MR3966582

Digital Object Identifier: 10.2969/aspm/08010043

Subjects:
Primary: 20G42, 46L37, 46L54, 81R50