Learning seminar on the basics of Temperley-Lieb algebras

Katarina Spasojevic, USRA, Department of Pure Mathematics, University of Waterloo

Abstract:  The aim of this learning seminar is to provide a gentle introduction to Temperley-Lieb algebras.  We will start with some enumeration of Temperley-Lieb diagrams, then we will discuss how these diagrams are organized into a monoid, out of which we obtain the Temperley-Lieb algebra $TL_n ( \beta )$.  This will be followed by studying some structural properties of $TL_n ( \beta )$, and its representations.  The sources used for the presentations are the monograph [1] listed below, and some survey papers that are available online, e.g. [2] below.

References:

[1]  Coxeter graphs and towers of algebras,  by F.M. Goodman, P. de la Harpe and V.F.R. Jones.  Volume 14 of MSRI Publications, Springer-Verlag, 1989.

[2]  An introduction to the representation theory of Temperley-Lieb algebras, by J. de Groot.  Bachelor's Thesis at the University of Amsterdam, 2015.

The seminar will meet on Zoom.

  Meeting ID: 947 3151 2522

  Passcode: 735851