401-3226-01L  Representation Theory of Lie Groups

SemesterFrühjahrssemester 2019
DozierendeP. D. Nelson
Periodizitätjährlich wiederkehrende Veranstaltung

KurzbeschreibungThis 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.
LernzielThe 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.
Inhalt* 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
LiteraturBekka, de la Harpe and Valette: "Kazhdan's Property (T)", Cambridge University Press.
Voraussetzungen / BesonderesDifferential geometry, Functional analysis, Introduction to Lie Groups (or equivalent).