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VOL. 46 | 2017 A formula for the Jones-Wenzl projections
Scott Morrison

Editor(s) Scott Morrison, David Penneys


I present a method of calculating the coefficients appearing in the Jones-Wenzl projections in the Temperley-Lieb algebras. It essentially repeats the approach of Frenkel and Khovanov in [4] published in 1997. I wrote this note mid-2002, not knowing about their work, but then set it aside upon discovering their article.

Recently I decided to dust it off and place it on the arXiv — hoping the self-contained and detailed proof I give here may be useful.

The proof is based upon a simplification of the Wenzl recurrence relation. I give an example calculation, and compare this method to the formula announced by Ocneanu [13] and partially proved by Reznikoff [15]. I also describe certain moves on diagrams which modify their coefficients in a simple way.


Published: 1 January 2017
First available in Project Euclid: 21 February 2017

zbMATH: 06990158
MathSciNet: MR3635675

Rights: Copyright © 2017, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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