Advanced Topics Course in Representation Theory
Contact Information
- Course Timing(Via Zoom): Tuesday & Thursday 2:00-3:30.
- Email: swarnava@math.tifr.res.in
- Discussion: If you want to discuss some aspects of this course or the material discussed, please feel free to sent me an email and set-up an appointment.
Course Description
In the first part of the course we will cover basics of representation
theory of Kac-Moody algebras focusing on the affine case. We will also
cover representation theory of Virasoro algebras and the Sugawara
construction. The second part of the course will use representations of
Kac-Moody algebras to construct and study conformal blocks following the
works of Tsuchiya-Ueno-Yamada.
Conformal blocks are vector bundles on the moduli space of curves that
satisfy phenomenal properties like ``factorization", ``propagation of
vacua" and are equipped with a flat projective connection
(WZW/TUY/Hitchin). Conformal blocks can also be realised as the space of
``non-abelian" theta functions i.e. as global sections of natural line
bundle on the moduli of G-bundles on curves. The Verlinde formula computes
the rank of the conformal blocks vector bundles.
Very basic knowledge of representation theory of Lie algebras and
algebraic geometry are prerequisites to attend the course.
Lecture Notes