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401-3226-01L  Unitary Representations of Lie Groups and Discrete Subgroups of Lie Groups

SemesterFrühjahrssemester 2016
DozierendeM. Einsiedler
Periodizitätjährlich wiederkehrende Veranstaltung
LehrspracheEnglisch


KurzbeschreibungThis course will contain three parts:
* Classification of simple Lie algebras
* Introduction to unitary representations of Lie groups
* Introduction to the study of discrete subgroups of Lie groups, the quotient space, and some applications.
LernzielThe 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.
Inhalt* Classification using Dynkin diagrams
* 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 / BesonderesFunctional analysis I and
Lie Groups I or Differential geometry I.