Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
Please read the published information on the individual courses carefully.

401-3226-01L  Representation Theory of Lie Groups

SemesterSpring Semester 2017
LecturersE. Kowalski
Periodicityyearly recurring course
Language of instructionEnglish


AbstractThis 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.
ObjectiveThe 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
LiteratureBekka, de la Harpe and Valette: "Kazhdan's Property (T)", Cambridge University Press.
Prerequisites / NoticeDifferential 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.