Department of Mathematics

Unitary Representations of Lie Groups and Discrete Subgroups of Lie Groups

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Prerequisites: Functional analysis I and either Lie Groups I or Differential geometry I.

Contents: This course will contain three parts:
* Classification of simple Lie algebras via Dynkin diagrams
* Introduction to unitary representations of Lie groups. For compact groups: Peter-Weyl theory, weights and Weyl character formula. Theory for SL(2,R) and SL(2,C). Property (T) for SL(n,R)
* Introduction to the study of discrete subgroups of Lie groups, the quotient space, and some applications.
The goal is to acquire familiarity with the basic formalism and results concerning Lie groups and their unitary representations, and to apply these to the study of discrete subgroups, especially lattices, in Lie groups.

Lecturer: Prof. Dr. Manfred Einsiedler
Assistant: Manuel Luethi


Wednesdays, 08.00 am to 10.00 am, HG G26.5
Fridays, 10.00 am to 12.00 pm HG G26.5


On Fridays, every second week: 10.00 am 12.00 am at HG 26.5, starting on 04.03.

Exercise sheets will be published on taskbase as the course progresses, allowing the students to deepen their understanding of the theory. There will be no Testat condition.


Bekka, de la Harpe and Valette: "Kazhdan's Property (T)", Cambridge University Press.


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© 2016 Mathematics Department | Imprint | Disclaimer | 19 May 2016