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.