Kolloquium des Graduiertenkollegs Gruppen
Prof. Gregg J. Zuckerman
"Cohomological induction in the representation theory of Lie algebras"
Ordinary induction from a subalgebra to an algebra
plays a fundamental role in the representation theory
of Lie algebras. However, in the theory of semisimple
Lie algebras over the complex numbers, the more
notion of cohomological induction yields infinite
dimensional modules which cannot be obtained by
ordinary induction. We will review this notion,
starting with its inception in the late 1970's up to
its recent applications to locally finite dimensional
Some references include Vogan's Representations of
Real Reductive Lie Groups, and Knapp and Vogan's
Cohomological Induction and Unitary Representations.
See also our joint work with Ivan Penkov at