School Seminars and Colloquia

Colloquium: Unitary representations of real Lie groups


by Professor Peter Trapa

Institution: Department of Mathematics, University of Utah
Date: Tue 7th April 2009
Time: 12:00 PM
Location: Russell Love Theatre, Richard Berry Bldg, The Uni of Melb

Abstract: Suppose G is a real reductive Lie group. In its purest form, abstract harmonic
analysis asks for a description of the unitary dual of G, the set of equivalence classes of
its irreducible unitary representations. For example, if G is the circle group, the unitary
dual amounts to the sines and cosines underlying Fourier series. On the other hand,
if G is the additive group of real numbers, the unitary dual amounts to the exponential
functions appearing in the theory of the Fourier transform. One of the outstanding
problems in the subject has been to describe the unitary dual of G in general. Recently
a new set of ideas has emerged which appears powerful enough to give such a
description under rather mild assumptions. This talk will give a history of the problem,
and will report on recent progress (joint with Adams, van Leeuwen, and Vogan).

For More Information: Contact Paul Pearce ( or Paul Norbury (

Colloquium Website