Programmeon Lie Groups 2001


Singular Unitary Representations and Applications


Professor Jian-Shu Li

Hong Kong University of Science & Technology, HK


A basic problem in representation theory is to understand the set of irreducible unitary representations of a given semi-simple Lie group G. For general G this problem remains largely unsolved. In these lectures we will try to present the theory of singular unitary representations which offers a certain amount of insight into an exotic part of the unitary dual of a given simple Lie group.

Globalization of this theory gives rise to some parallel understanding of a small part of the spectrum of automorphic forms. The arithmetic significance is not yet clear. We willl discuss some applications, including the determination of the first eigenvalue of Laplacian for arithmetic manifolds, and vanishing and non-vanishing results for the cohomology of the same objects.

Dates / Time:

4:00 - 5:00pm Wednesdays and  Fridays, April18 - 27, 2001


Room 517, Meng Wah Complex