Affine Kac-Moody Lie Algebras (Evgeny Feigin )

Exam.  exam_15.12.pdf

Lectures:
15.09. Fundamental representations of the Lie algebra of infinite matrices.
22.09. The Japanese cocylce and the Heisenberg algebra.
06.10.  Realizations of the generalized Cartan matrices; generators-relations construction.
20.10. Kac-Moody algebras: definition and basic properties.
27.10. Generalized Cartan matrices of finite, affine and indefinite types.
03.11. Equivalence of definitions of types of generalized Cartan matrices.
10.11. Classification of affine Cartan matrices.
17.11. Canonical central element and basic imaginary root.
24.11. Loop algebras and central extensions.
01.12. Central extensions and affine GCM.
08.12. Weyl group of a Kac-Moody algebra.
15.12. Affine Weyl groups.
22.12. Vertex operator realization of basic representation.

Final results.
affine_17.xls

Homeworks:
Homework 1 (due 04.10)  hwork_22.09.pdf
Homework 2 (due 18.10)  hwork_07.10.pdf
Homework 3 (due 01.12)  hwork_24.11.pdf

Ten minutes problems.
22.09.  10min_22.09.pdf
06.10.  10min_06.10.pdf
20.10.  10min_20.10.pdf
27.10.  10min_27.10.pdf
03.11.  10min_03.11.pdf
17.11.  10min_17.11.pdf
24.11.  10min_24.11.pdf
01.12.  10min_01.12.pdf
08.12.  10min_08.12.pdf
15.12.  10min_15.12.pdf

Books:
V. Kac, Infinite dimensional Lie algebras, Cambridge University Press.
R.Carter, Lie Algebras of Finite and Affine Type, Cambridge Studies in Advanced Mathematics .
Kac V., Raina A., Rozhkovskaya N., Bombay lectures on Highest weight representations of infinite dimensional Lie algebras.