Representation Theory of Lie Groups Spring 2019

Paul D. Nelson
Subhajit Jana

The tentative outline will be as follows. Basic representation theory of compact groups (Peter-Weyl theorem, etc.) and compact Lie groups (Weyl character formula, etc.), branching problems, algebraic representations of reductive groups, basics on admissible and tempered representations of reductive groups (parabolic induction, Langlands classification, etc.), with emphasis on illustrative examples (U(n), GL(n,C), SL(2,R), etc.)


Lie group I, a bit of functional analysis. Representation theory of finite groups would be helpful, but not assumed.

Course Notes

  • This is Lie Group course note taught by Prof. Nelson in Autumn 2016.
  • The course note. Last updated on 15th July 10:30.
  • This file (last updated 20th August 13:50) contains exercises and solutions. This file will be updated regularly with new exercises and solutions to the old exercises. There will be exercise classes, approximately bi-weekly, replacing lecture hours.

    The next exercise class will be on 9th May.

    LectureTuesday 10:00-12:00HG E 33.1
    LectureThursday 08:00-10:00HG G 5