Harish-Chandra Conference Abstract

Anthony W. Knapp

Abstract of "Intertwining operators and small unitary representations"

In several authors' attempts to classify the irreducible unitary representations of semisimple Lie groups, representations that are "small" play a pivotal role. The trouble is that there are too many small representations for the unitarity of all of them to be decided by direct calculations. This article proposes a technique for combining the use of intertwining operators and cohomological induction to reduce the investigation of all small representations to the investigation of just a few of them. It illustrates the technique by giving applications to analytic continuations of discrete series, both holomorphic and nonholomorphic. It includes a certain amount of expository background concerning discrete series, analytic continuations thereof, and cohomological induction.