2006-11-03

Paul Friedman, Union College

Langlands Parameters and Cohomological Induction

One of the aims of representation theory is to classify all unitary irreducible representations of a semisimple Lie group. These representations lie within of a larger class of representations called admissible representations, which have been classified by Langlands, Knapp and Zuckerman in terms of so-called Langlands parameters. Since not all admissible representations are unitary, it is important to determine the Langlands parameters of the unitary representations. Cohomological induction, developed by Zuckerman and Vogan, is an important algebraic technique known to produce many unitary representations. In this talk, we will discuss one way to identify a set of Langlands parameters of modules of cohomological induction.