Instructor: Alexis Langlois-Rémillard
Examination: Exams will be oral on topics of the course; they will take place on the last week of July (28-31 July). Later in the semester you will be able to book a 45min spot to take it.
A preliminary plan is available here.
Office hours: Monday 10-11 (just after the course), or on appointement. Office 4.042 of Math Zentrum. (If you want to take your chance you can come to my office Monday-Thursday 11-17 and I should be there, but send an email to be sure as I sometimes go to seminar and work elsewhere.)
The following lecture notes give roughly what we followed from the book and provide the extra material I extracted from other sources (Mainly Mathas' book Iwahori-Hecke algebras and Schur algebras of the symmetric group).
05.05.2025 We covered a bit of cellular algebra theory. I've written up the notes in the exercise sheet with some extra details on the proofs we did not do in class.
28.04.2025 In this lecture, I have given a bit on the physical motivation of the TL algebras and variations. It's a bit hard to suggest good reference on this. I suggest: P. Martin, Potts Models and Related Problems in Statistical Mechanics, Volume 5 of Advances in Statistical Mechanics. World Scientific,Singapore, 1991. and R. Baxter, Exactly Solved Models in Statistical Mechanics. Academic Press, London, 1982. The scanned course notes might help.
14.04.2025 In this lecture, we followed Ridout and Saint-Aubin. Standard modules, induction and the structure of the Temperley-Lieb algebra. Adv. Theo. Math. Phys. 18.5 pp 957-1041 (2014) https://dx.doi.org/10.4310/ATMP.2014.v18.n5.a1.
Notes of the lectures will appear here. We will be roughly following Chris Bowman's book «Diagrammatic algebra» (to appear). In general, I will only provide notes when I depart from the book. A (virtual) copy of the book will be shared with students at the first lecture (thanks Chris!) and we will take bits and pieces from other sources. You can email me for the pdf of the course.
Each week, a few problems will be given out. I do not expect you to do all of them, but I will assume you read them. Exercises are either from the book or from different sources. I will be more than happy to discuss solutions either at the office, before or after the course, or via email.