Spring 2006, Course 18.747: Infinite dimensional Lie algebras

TR 1-2:30, Rm. 2-255

Instructors Roman Bezrukavnikov, Pavel Etingof^{1}

Office 2-284; 2-176

Telephone 253-2684; 253-3669

Email bezrukav@math.mit.edu, etingof@math.mit.edu

The course will be devoted to a detailed introduction, with proofs, into the structure and representation theory of some of the most imprortant infinite dimensional Lie algebras – Heisenberg algebras, Kac-Moody algebras, Virasoro algebra. The books for the course are Kac and Raina ”Highest weight representations of infinite dimensional Lie algebras” and Kac ”Infinite dimensional Lie algebras”. We will also use an expository paper by Feigin and Zelevinsky that will be distributed in class. We will start with Kac-Moody algebras (starting with a reminder on the finite dimensional case) and discuss their structure and representation theory, including character formulas and Kac-Macdonald identities. We will then go to the book of Kac and Raina and discuss representations of the Heisenberg algebra, Virasoro algebra, affine sl(n), and relation to integrable systems. To officially pass the course, it will be required to solve homework assignments which will be assigned on Thursday and due the following Thursday.

1The first half of the course will be taught by R.B, the second one by P.E.