401-3226-01L Representation Theory of Lie Groups
|Semester||Spring Semester 2017|
|Periodicity||yearly recurring course|
|Language of instruction||English|
|Abstract||This course will contain two parts:|
* Introduction to unitary representations of Lie groups
* Introduction to the study of discrete subgroups of Lie groups and some applications.
|Objective||The goal is to acquire familiarity with the basic formalism and results concerning unitary representations of Lie groups, and to apply these to the study of discrete subgroups, especially lattices, in Lie groups.|
|Content||* Unitary representations of compact Lie groups: Peter-Weyl theory, weights, Weyl character formula|
* Introduction to unitary representations of non-compact Lie groups: the examples of SL(2,R), SL(2,C)
* Example: Property (T) for SL(n,R)
* Discrete subgroups of Lie groups: examples and some applications
|Literature||Bekka, de la Harpe and Valette: "Kazhdan's Property (T)", Cambridge University Press.|
|Prerequisites / Notice||Differential geometry, Functional analysis, Introduction to Lie Groups (or equivalent).|
Notice that this course has a large overlap with 401-3226-01L Unitary Representations of Lie Groups and Discrete Subgroups of Lie Groups taught in FS 2016. Therefore it is not possible to acquire credits for both courses.