| Abstract:
Several cohomological approaches to the study of
representations of real semisimple Lie groups emerged from the
attempts to generalize the classical Borel-Weil-Bott theorem which
gives the construction of irreducible representations of compact Lie
groups. A completely algebraic approach was started by Zuckerman
and it is known now as "cohomological induction". A more geometric
approach, using sheaf cohomology and D-module theory, was developed
by Beilinson and Bernstein. A connection between these approaches
was established in the duality theorem of Hecht, Schmid, Wolf and
Milicic. In this talk we are going to describe how, using the right
homological algebra machinery, one can establish a natural relation
between these two approaches which explains the duality theorem. |
alexsuciu@neu.edu