ICTS-TIFR Bengaluru

Lectures on
representations of
quantum affine algebras

Arun Ram

November 2023

Lectures

Lecturer: Arun Ram, University of Melbourne, email: aram@unimelb.edu.au

Time and Location of the Lectures: ICTS-TIFR Bengaluru 13-18 November 2023

Overview

The goal of this lecture series is to provide a view of the integrable representations of quantum affine algebras.

It is a pleasure to deliver these lectures in honor of Professor Vyjayanthi Chari, whose contribution has been fundamental in the development of the subject.

References

The lectures will largely be based on section 2 of the following survey paper where further references can be found.

Positive level, negative level and level zero, (with Finn McGlade and Yaping Yang), appeared in the special volume in conjuction with the conference International Festival in Schubert Calculus, Sun-Yat Sen University, Guangzhou China, 5-11 November 2017, Schubert calculus and its applications in combinatorics and representation theory, Springer Proc. Math. Stat. 332, Springer, Singapore (2020) 153-194, MR4167516, arXiv1907.11796.

Lecture Plan

Lecture 1, Examples of U-modules: Tentative lecture notes for Lecture 1
Lecture 2, The affine Weyl group: Tentative lecture notes for Lecture 2
Lecture 3, Extremal weight modules: Tentative lecture notes for Lecture 3
Lecture 4, Level 0: Tentative lecture notes for Lecture 4
Lecture 5, R-matrices:
Lecture 6, Presentations:

Problem sheets

Problem sheets and solutions should be made by the students and I will post them here

Problem sheet 1:
Problem sheet 2:
Problem sheet 3:
Problem sheet 4:
Problem sheet 5:
Problem sheet 6: