Title: Real Semisimple Lie Groups
Lecturer: Prof. R. Parthasarathy (TIFR).

Wednesdays and Fridays 2:00-3:15pm, room 217.

Course description:

Verma Modules as in Chapter 7 of Dixmier (Enveloping algebras) (~3 lects);

Cohomologically induced representations (Enright-Varadarjan construction,
generalisations of the above.) (~4 lects);

Zuckerman's derived functor construction of the above (~2 lects);

Calculation of the cohomology of compact locally symmetric spaces
{Matsushima's formula, square of the Dirac operator, Spin module,
Dirac operator inequality, Kumaresan's paper} (4++ lects);

Criterion for unitarisability of highest weight modules: (~3 lects);

HC's Discrete Series I;  Discrete Series II: V.S.Vardarajan's
exposition + Geometric realisation of the above (~8 lects).