Affine Kac-Moody Lie algebras and applications

Evgeny Feigin

Announcements.
Exam problems available (due 15.12)
Homework 3 (due 24.11) is available (new version, misprints corrected).
Important: Lecture 27.10 (only), new time: 18.30.
Homework 2 (due 27.10) is available.

Textbooks:
1. A. Kirillov Jr, An Introduction to Lie Groups and Lie Algebras.
2.. R.W. Carter, Lie Algebras of Finite and Affine Type.
3. V.Kac,  Innite dimensional Lie algebras.
4. V.Kac, A.Raina,  Bombay lectures on Highest weight representations of infite-dimensional Lie algebras
5. P.Di Francesco, P. Mathieu, D.Senechal, Conformal Field Theory.

Lectures.

Lecture 1, 15.09. Finite-dimensional simple Lie algebras: Cartan subalgebras, root vectors and Cartan decomposition. 
Lecture 2, 22.09. Finite-dimensional simple Lie algebras: Weyl group, Cartan matrix, Dynkin diagram.
Lecture 3, 29.09. Finite-dimensional simple Lie algebras: Verma modules, irreducible representations, characters.
Lecture 4, 06.10. Generalized Cartan matrices, Kac-Moody Lie algebras - first approximation.
Lecture 5, 13.10. Kac-Moody Lie algebras - definitions and first properties..
Lecture 6, 20.10. Finite, Affine and Indefinite Kac-Moody Lie algebras.
Lecture 7, 27.10. Classification of affine Kac-Moody Lie algebras.
Lecture 8, 03.11. Weyl group and invariant bilinear form.
Lecture 9, 10.11. Real and imaginary roots.
Lecture 10, 17.11. Canonical central element and imaginary roots for affine Lie algebras.
Lecture 11, 24.11. Center and the Weyl group for affine Lie algebras.
Lecture 12, 01.12. Weyl group for affine Lie algebras and alcoves.
Lecture 13, 08.12. Affine walls and alcoves.
Lecture 14, 15.12. Loop algebras and central extensions.

Ten minutes problems.

affine_10min_15.09 (PDF, 85 Кб)   

affine_10min_22.09 (PDF, 86 Кб)

 affine_10min_29.09 (PDF, 70 Кб)

 affine_10min_06.10 (PDF, 41 Кб)

 affine_10min_13.10 (PDF, 125 Кб)

 affine_10min_20.10 (PDF, 76 Кб)

 affine_10min_27.10 (PDF, 41 Кб)

 affine_10min_03.11 (PDF, 83 Кб)

affine_10min_10.11 (PDF, 112 Кб)

affine_10min_17.11 (PDF, 81 Кб)

affine_10min_24.11 (PDF, 81 Кб)

affine_10min_01.12 (PDF, 39 Кб)



affine_10min_08.12 (PDF, 100 Кб)

affine_10min_15.12 (PDF, 62 Кб)

 

Homeworks.

29.09.   hwork_29.09 (PDF, 141 Кб)
21.10.   hwork_21.10 (PDF, 99 Кб)   due 27.10.
18.11.             hwork_18.11 (PDF, 101 Кб)            due 24.11.

Exam.

08.12.  exam_08.12 (PDF, 91 Кб)

Grades.

 grades_21.12 (XLS, 39 Кб)