Representations of affine and vertex operator algebras (E. Feigin)

Exam (due December 15)

 Exam (PDF, 138 Кб)

Lectures

15.09. Lecture 1.  Heisenberg algebra and Fock modules.
22.09. Lecture 2. Semi-infinite wedge space.
29.09. Lecture 3. $a_\infty$ and one-dimensional central extension.
06.10. Lecture 4. Embedding of the Heisenberg algebra into $a_\infty$. Witt algebra. 
13.10. Lecture 5. Central extensions of the Witt algebra. Charge 0 and 1 representations of the Virasoro algebra. 
20.10. Lecture 6. Bosonization of the Virasoro algebra. Verma modules and irreducible highest weight modules.
27.10. Lecture 7. Boson-fermion correspondence.
03.11. Lecture 8. Wedging and contracting operators, vertex operators.
10.11. Lecture 9. Schur polynomials.
24.11. Lecture 10. Affine gl(n).
01.12. Lecture 11. Fundamental representations of affine sl(n).
08.12. Lecture 12. q-characters and principal grading.
15.12. Lecture 13. Principal vertex operator realization and VOA.

Homeworks

 hw1 (PDF, 126 Кб)      (due  03.11)

 hw2 (PDF, 121 Кб)      (due  24.11)

 

Ten-minutes problems

 voa_10min_15.09 (PDF, 71 Кб)

 voa_10min_22.09 (PDF, 59 Кб)

 voa_10min_29.09 (PDF, 62 Кб)

 voa_10min_06.10 (PDF, 68 Кб)

 voa_10min_13.10 (PDF, 69 Кб)

 voa_10min_20.10 (PDF, 83 Кб)

 voa_10min_27.10 (PDF, 76 Кб)

 voa_10min_03.11 (PDF, 49 Кб)

 voa_10min_10.11 (PDF, 79 Кб)

 voa_10min_24.11 (PDF, 90 Кб)

 voa_10min_01.12 (PDF, 105 Кб)

 voa_10min_08.12 (PDF, 103 Кб)

 voa_10min_15.12 (PDF, 105 Кб)

Results

 results_final (XLS, 35 Кб)

 

Books for the course

Kac V., Raina A.  Bombay lectures on Highest weight representations of infinite dimensional Lie algebras.
Kac, V.  Infinite dimensional Lie algebras.
Frenkel E., Ben-Zwi D. Vertex algebras and algebraic curves.
Kac V. Vertex algebras for beginners.