Kolloquium des Graduiertenkollegs Gruppen und Geometrie

Donnerstag, 03.05.2007

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 general 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 Lie algebras. 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 math.iu-bremen.de/penkov.