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.
Lernziel
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.
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
Literatur
Bekka, de la Harpe and Valette: "Kazhdan's Property (T)", Cambridge University Press.
Voraussetzungen / Besonderes
Differential geometry, Functional analysis, Introduction to Lie Groups (or equivalent).
Leistungskontrolle
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs