Infinite-Dimensional Lie Algebras and Integrable Systems Spring 2025

Lecturer

Denis Nesterov

Location and Time

Lecture: Thursday 10:15-12:00, HG G 26.5

Office hours: Thursday 2:00-3:00, HG J 14.6 (or send me an email)

Content

The course is an introduction to the representation theory of infinite-dimensional Lie algebras, focusing on the Lie algebra of infinite matrices. The aim is to understand the Kadomtsev–Petviashvili equation using representation-theoretic methods. This equation exemplifies Integrable systems, a class of differential equations with rich symmetries enabling exact solutions.

Lecture Notes

Exercises

Exercise sheet	Solutions
Exercise sheet 1
Exercise sheet 2
Exercise sheet 3
Exercise sheet 4
Exercise sheet 5
Exercise sheet 6
Exercise sheet 7
Exercise sheet 8

Literature

V. Kac, A.K. Raina and N. Rozhkovskaya, Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras, 2nd Edition, Advanced Series in Mathematical Physics: Volume 29
T. Miwa, M. Jimbo and E. Date, Solitons: Differential Equations, Symmetries and Infinite Dimensional Algebras, Cambridge University Press
N. J. Hitchin, G. B. Segal, and R. S. Ward, Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces, Oxford University Press