Infinite dimensional Lie algebras
Student No.:50
Time:Wed 10:10-12:00, 2017-02-20~ 2017-06-02 (No classes on public holidays)
Instructor:Daniele Valeri  [Tsinghua University]
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-2-20
Ending Date:2017-6-2



The  course  will  be  devoted  to  an introduction to the structure and representation theory of some of the most important infinite dimensional Lie algebras: Heisenberg algebras, Virasoro algebra and Kac-Moody algebras.

In the first part we will discuss representations of the Heisenberg algebra, Virasoro algebra, affine sl(n), and relations to integrable systems.

In the second part we will discuss the structure and representation theory of Kac-Moody algebras, including character formulas and Kac-Macdonald identities.



Linear algebra.



- V. G. Kac  and  A.  Raina, Highest  weight representations of infinite dimensional Lie algebras;

- B.L. Feigin and A.V. Zelevinsky, Representations of contragradient Lie algebras and the Kac-Macdonald identities.